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1l6i1glss | physics | magnetics | magnetic-moment | <p>Two concentric circular loops of radii $$r_{1}=30 \mathrm{~cm}$$ and $$r_{2}=50 \mathrm{~cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7 \mathrm{~A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops ... | [{"identifier": "A", "content": "$$\\frac{7}{2} \\hat{k} \\,\\mathrm{Am}^{2}$$"}, {"identifier": "B", "content": "$$-\\frac{7}{2} \\hat{k} \\,\\mathrm{Am}^{2}$$"}, {"identifier": "C", "content": "$${7}\\, \\hat{k} \\,\\mathrm{Am}^{2}$$"}, {"identifier": "D", "content": "$${-7}\\, \\hat{k} \\,\\mathrm{Am}^{2}$$"}] | ["B"] | null | <p>$${\mu _1} = \pi r_1^2 \times {I_1}$$</p>
<p>$${\mu _2} = \pi r_2^2 \times {I_2}$$</p>
<p>$$\therefore$$ $${\mu _{net}} = ({\mu _2} - {\mu _1})\left( { - \widehat k} \right)$$</p>
<p>$$ = \pi \left( {r_2^2 - r_1^2} \right)I\left( { - \widehat k} \right)$$</p>
<p>$$ = 3.142 \times \left( {{{0.5}^2} - {{0.3}^2}} \righ... | mcq | jee-main-2022-online-26th-july-evening-shift | 11,934 |
1l6p6c1fz | physics | magnetics | magnetic-moment | <p>A wire of length $$314 \mathrm{~cm}$$ carrying current of $$14 \mathrm{~A}$$ is bent to form a circle. The magnetic moment of the coil is ________ A $$-\mathrm{m}^{2}$$. [Given $$\pi=3.14$$]</p> | [] | null | 11 | <p>$$R = {l \over {2\pi }} = {{314} \over {2 \times 3.14}} = 50$$ cm</p>
<p>$$\mu = \pi {R^2}i$$</p>
<p>$$ = 14 \times 3.14 \times {(0.5)^2}$$</p>
<p>$$ = 11$$ A-m<sup>2</sup></p> | integer | jee-main-2022-online-29th-july-morning-shift | 11,935 |
1ldpkb8vo | physics | magnetics | magnetic-moment | <p>A rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4 \mathrm{~A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4 \pi \times 10^{-6} \mathrm{~Wb}$$. The relative ... | [{"identifier": "A", "content": "$$\\frac{5}{16}$$"}, {"identifier": "B", "content": "125"}, {"identifier": "C", "content": "$$\\frac{32}{5}$$"}, {"identifier": "D", "content": "12.5"}] | ["A"] | null | Magnetic field in the Solenoid,
<br/><br/>$$
\begin{aligned}
& \mathrm{B}=\mu_0 \mu_r \mathrm{nI} \\\\
& \text { Magnetic flux, } \phi=\mathrm{N}(\mathrm{BA}) \\\\
& \phi=N\left(\mu_0 \mu_r n I A\right) \\\\
& \Rightarrow 4 \pi \times 10^{-6}=400\left(4 \pi \times 10^{-7} \mu_r \times \frac{400}{0.4} \times 0.4 \times ... | mcq | jee-main-2023-online-31st-january-morning-shift | 11,936 |
1ldr26gfm | physics | magnetics | magnetic-moment | <p>The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $$\mathrm{r}_{\mathrm{A}}=10$$ $$\mathrm{cm}$$ and $$\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$$ respectively are equal if : (Where $$\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$$ and $$\mathrm{N}_{\m... | [{"identifier": "A", "content": "$$4 \\mathrm{~N}_{\\mathrm{A}} \\mathrm{I}_{\\mathrm{A}}=\\mathrm{N}_{\\mathrm{B}} \\mathrm{I}_{\\mathrm{B}}$$"}, {"identifier": "B", "content": "$$2 \\mathrm{~N}_{\\mathrm{A}} \\mathrm{I}_{\\mathrm{A}}=\\mathrm{N}_{\\mathrm{B}} \\mathrm{I}_{\\mathrm{B}}$$"}, {"identifier": "C", "conten... | ["D"] | null | <p>$$M_A=M_B$$</p>
<p>$${I_A}{N_A}\left( {\pi r_A^2} \right) = {I_B}{N_B}\left( {\pi r_B^2} \right)$$</p>
<p>$${I_A}{N_A} = 4{I_B}{N_B}$$</p> | mcq | jee-main-2023-online-30th-january-morning-shift | 11,937 |
1ldtzeohw | physics | magnetics | magnetic-moment | <p>For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $$4.0\times10^{-5}\mathrm{N~m~rad^{-1}}$$, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in cm$$^2$$) i... | [{"identifier": "A", "content": "1.5"}, {"identifier": "B", "content": "2.0"}, {"identifier": "C", "content": "0.5"}, {"identifier": "D", "content": "1.0"}] | ["D"] | null | $\because \theta=\left(\frac{N B A}{K}\right) I$
<br/><br/>
$$
\begin{aligned}
A & =\frac{\theta K}{N B I} \\\\
& =\frac{0.05 \times 4 \times 10^{-5}}{(200) \times(0.01) \times\left(10 \times 10^{-3}\right)} \\\\
& =1 \mathrm{~cm}^{2}
\end{aligned}
$$
| mcq | jee-main-2023-online-25th-january-evening-shift | 11,938 |
luxwem58 | physics | magnetics | magnetic-moment | <p>A straight magnetic strip has a magnetic moment of $$44 \mathrm{~Am}^2$$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $$\mathrm{Am}^2$$.</p>
<p>(given $$\pi=\frac{22}{7}$$)</p> | [] | null | 28 | <p>Magnetic moment is defined as the product of the magnet's pole strength and the distance between the poles (also known as the magnetic length). When a magnetic strip is bent, its magnetic moment changes based on the new configuration.</p>
<p>Consider a straight magnetic strip with a magnetic moment of $$44 \, \text... | integer | jee-main-2024-online-9th-april-evening-shift | 11,939 |
WoHSqfJ9YhjtYb6d | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its | [{"identifier": "A", "content": "speed "}, {"identifier": "B", "content": "mass "}, {"identifier": "C", "content": "charge "}, {"identifier": "D", "content": "magnetic induction "}] | ["A"] | null | <b>KEY CONCEPT :</b> The time period of a charged particle
<br><br>$$\left( {m,q} \right)$$ moving in a magnetic field $$(B)$$ is $$T = {{2\pi m} \over {qB}}$$
<br><br>The time period does not depend on the speed of the particle. | mcq | aieee-2002 | 11,942 |
oz4aSIdP398XDmLy | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | If an electron and a proton having same momentum enter perpendicular to a magnetic field, then | [{"identifier": "A", "content": "curved path of electron and proton will be same (ignoring the sense of revolution) "}, {"identifier": "B", "content": "they will move undeflected "}, {"identifier": "C", "content": "curved path of electron is more curved than that of the proton "}, {"identifier": "D", "content": "path o... | ["A"] | null | <b>KEY CONCEPT : </b> When a charged particle enters perpendicular to a magnetic field,
<br><br>then it moves in a circular path of radius.
<br><br>$$r = {p \over {qB}}$$
<br><br>where $$q=$$ Charge of the particle
<br><br>$$p=$$ Momentum of the particle
<br><br>$$B=$$ Magnetic field
<br><br>Here $$p,q$$ and $$B$$ are... | mcq | aieee-2002 | 11,943 |
v0t6m0y8QTPXGOyR | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\overrightarrow v $$ describe a circular path of radius $$R$$ when subjected to a uniform transverse magnetic field of induction $$B.$$ The network done by the field when the particle completes one full circle is | [{"identifier": "A", "content": "$$\\left( {{{M{v^2}} \\over R}} \\right)2\\pi R$$ "}, {"identifier": "B", "content": "zero "}, {"identifier": "C", "content": "$$B\\,\\,Q\\,2\\pi R$$ "}, {"identifier": "D", "content": "$$B\\,Qv\\,2\\pi R$$ "}] | ["B"] | null | The work done, $$dW = Fds\,\cos \,\theta $$
<br><br>The angle between force and displacement is $${90^ \circ }.$$
<br><br>Therefore work done is zero. | mcq | aieee-2003 | 11,944 |
Ut3FfAhiljX1f0sO | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle of charge $$ - 16 \times {10^{ - 18}}$$ coulomb moving with velocity $$10m{s^{ - 1}}$$ along the $$x$$-axis enters a region where a magnetic field of induction $$B$$ is along the $$y$$-axis, and an electric field of magnitude $${10^4}V/m$$ is along the negative $$z$$-axis. If the charged particle continues m... | [{"identifier": "A", "content": "$${10^3}Wb/{m^2}$$ "}, {"identifier": "B", "content": "$${10^5}Wb/{m^2}$$ "}, {"identifier": "C", "content": "$${10^{16}}Wb/{m^2}$$ "}, {"identifier": "D", "content": "$${10^{ - 3}}Wb/{m^2}$$ "}] | ["A"] | null | The situation is shown in the figure.
<br><br>$${F_E} = $$ Force due to electric field
<br><br>$${F_B} = $$ Force due to magnetic field
<br><br>It is given that the charged particle remains moving along $$X$$-axis (i.e. undeviated).
<br><br>Therefore $${F_B} = {F_E}$$
<br><br>$$ \Rightarrow qvB = qE$$
<br><br>$$ \Righ... | mcq | aieee-2003 | 11,945 |
fMKsHQ9vzJQezDA8 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of radius $$r$$ that is perpendicular to a magnetic field $$B.$$ The time taken by the particle to complete one revolution is | [{"identifier": "A", "content": "$${{2\\pi {q^2}B} \\over m}$$ "}, {"identifier": "B", "content": "$${{2\\pi mq} \\over B}$$ "}, {"identifier": "C", "content": "$${{2\\pi m} \\over {qB}}$$ "}, {"identifier": "D", "content": "$${{2\\pi qB} \\over m}$$ "}] | ["C"] | null | Equating magnetic force to centripetal force.
<br><br>$${{m{V^2}} \over r} = qvB\,\sin \,{90^ \circ }$$
<br><br>Time to complete one revolution.
<br><br>$$T = {{2\pi r} \over v} = {{2\pi m} \over {qB}}$$ | mcq | aieee-2005 | 11,947 |
v8i5CSQx8aqHN0vI | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarrow E $$ and $$\overrightarrow B $$ with a velocity $$\overrightarrow v $$ perpendicular to both $$\overrightarrow E $$ and $$\overrightarrow B, $$ and comes out without any change in magnitude or dire... | [{"identifier": "A", "content": "$$\\overrightarrow v = \\overrightarrow B \\times \\overrightarrow E /{E^2}$$ "}, {"identifier": "B", "content": "$$\\overrightarrow v = \\overrightarrow E \\times \\overrightarrow B /{B^2}$$ "}, {"identifier": "C", "content": "$$\\overrightarrow v = \\overrightarrow B \\times \\o... | ["B"] | null | Here, $$\overrightarrow E $$ and $$\overrightarrow B $$ are perpendicular to each other and the velocity $$\overrightarrow v $$ does not change; therefore
<br><br>$$qE = qvB \Rightarrow v = {E \over B}$$
<br><br>Also, $$\left| {{{\overrightarrow E \times \overrightarrow B } \over {{B^2}}}} \right| = {{E\,\,B\sin \thet... | mcq | aieee-2007 | 11,949 |
mR02r09kEHwQ2JAA | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A charged particle moves through a magnetic field perpendicular to its direction. Then | [{"identifier": "A", "content": "Kinetic energy changes but the momentum is constant "}, {"identifier": "B", "content": "the momentum changes but the kinetic energy is constant "}, {"identifier": "C", "content": "both momentum and kinetic energy of the particle are not constant "}, {"identifier": "D", "content": "both ... | ["B"] | null | <b>NOTE :</b> When a charged particle enters a magnetic field at a direction perpendicular to the direction of motion, the path of the motion is circular. In circular motion the direction of velocity changes at every point (the magnitude remains constant).
<br><br>Therefore, the tangential momentum will change at ever... | mcq | aieee-2007 | 11,950 |
jxdyQ6JihE8vcBRQJbQFO | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | In a certain region static electric and magnetic fields exist. The magnetic field is given by $$\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)$$ . If a test charge moving with a velocity $$\overrightarrow \upsilon = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right... | [{"identifier": "A", "content": "$$\\overrightarrow E = - {\\upsilon _0}\\,{B_0}\\left( {3\\widehat i - 2\\widehat j - 4\\widehat k} \\right)$$ "}, {"identifier": "B", "content": "$$\\overrightarrow E = - {\\upsilon _0}\\,{B_0}\\left( {\\widehat i + \\widehat j + 7\\widehat k} \\right)$$"}, {"identifier": "C", "con... | ["D"] | null | Here test charge experience no net force, So, sum of electric and magnetic field is zero.
<br><br>$$\therefore\,\,\,$$ F<sub>e</sub> + F<sub>m</sub> = 0
<br><br>$$\therefore\,\,\,$$ F<sub>e</sub> = $$-$$ q ($$\overrightarrow v $$ $$ \times $$ $$\overrightarrow B)$$
<br><br>= $$-$$ qB<sub>0</sub> $$\upsilon $$<sub>0</s... | mcq | jee-main-2017-online-8th-april-morning-slot | 11,952 |
YG1ipWqGon3ZiT8o | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of
radii r<sub>e</sub>, r<sub>p</sub>, r$$_\alpha$$ respectively in a uniform magnetic field B. The relation between r<sub>e</sub>, r<sub>p</sub>, r$$_\alpha$$ is: | [{"identifier": "A", "content": "r<sub>e</sub> < r$$_\\alpha$$ < r<sub>p</sub>"}, {"identifier": "B", "content": "r<sub>e</sub> > r<sub>p</sub> = r$$_\\alpha$$"}, {"identifier": "C", "content": "r<sub>e</sub> < r<sub>p</sub> = r$$_\\alpha$$"}, {"identifier": "D", "content": "r<sub>e</sub> < r<sub>p</sub>... | ["C"] | null | When a charged particle moves in a magnetic field then the charged particle moves in a circular path. So,
<br><br>$${{m{v^2}} \over r}$$ = Bqv
<br><br>$$ \Rightarrow $$$$\,\,\,$$ r = $${{mv} \over {Bq}}$$
<br><br>We know kinetic energy, K = $${1 \over 2}$$ mv<sup>2</sup>
<br><br>$$\therefore\,\,\,$$ mv = $$\sqrt {2... | mcq | jee-main-2018-offline | 11,953 |
hGv8KjfmOp16zCFU9zh5r | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $$ \times $$ 10$$-$$<sup>19</sup>C) | [{"identifier": "A", "content": "9.1 $$ \\times $$ 10<sup>$$-$$31</sup> kg"}, {"identifier": "B", "content": "1.6 $$ \\times $$ 10<sup>$$-$$27</sup> kg"}, {"identifier": "C", "content": "1.6 $$ \\times $$ 10<sup>$$-$$19</sup> kg"}, {"identifier": "D", "content": "2.0 $$ \\times $$ 10<sup>$$-$$24</sup> kg"}] | ["D"] | null | Given,
<br>radius of circular path(r) = 0.5 cm
<br>Magnetic field (B) = 0.5 T
<br>Electric field (E) = 100 V/m
<br><br>Charge of particle (q) = 1.6$$ \times $$10<sup>$$-$$19</sup> C
<br><br>As particle is moving in a circular path so,
<br><br>$${{m{v^2}} \over r} = qvB$$
<br><br>$$ \Rightarrow $$ r = $${{mv... | mcq | jee-main-2019-online-9th-january-evening-slot | 11,954 |
teeU6YJyPE1qwtbOggba5 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 $$ \times $$ 10<sup>–19</sup> C Mass of the electron = 9.1 $$ \times $$ 10<sup>–31</sup> kg] | [{"identifier": "A", "content": "7.5 $$ \\times $$ 10<sup>$$-$$4</sup> m"}, {"identifier": "B", "content": "7.5 $$ \\times $$ 10<sup>$$-$$3</sup> m"}, {"identifier": "C", "content": "7.5 m"}, {"identifier": "D", "content": "7.5 $$ \\times $$ 10<sup>$$-$$2</sup> m"}] | ["A"] | null | $$r = {{\sqrt {2mk} } \over {eB}} = {{\sqrt {2me\Delta v} } \over {eB}}$$
<br><br>$$r = {{\sqrt {{{2m} \over e}.\Delta v} } \over B} = {{\sqrt {{{2 \times 9.1 \times {{10}^{ - 31}}} \over {1.6 \times {{10}^{ - 19}}}}\left( {500} \right)} } \over {100 \times {{10}^{ - 3}}}}$$
<br><br>$$r = {{\sqrt {{{9.1} \over {0.16}} ... | mcq | jee-main-2019-online-11th-january-morning-slot | 11,955 |
iAmybRMkOBHuVkSVj1SOR | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | The region between y = 0 and y = d contains a magnetic field $$\overrightarrow B = B\widehat z$$. A particle of mass m and charge q enters the region with a velocity $$\overrightarrow v = v\widehat i.$$ If d $$=$$ $${{mv} \over {2qB}},$$ the acceleration of the charged particle at the point of its emergence at the o... | [{"identifier": "A", "content": "$${{qvB} \\over m}\\left( -{{{\\sqrt 3 } \\over 2}\\widehat i - {1 \\over 2}\\widehat j} \\right)$$"}, {"identifier": "B", "content": "$${{qvB} \\over m}\\left( {{1 \\over 2}\\widehat i - {{\\sqrt 3 } \\over 2}\\widehat j} \\right)$$"}, {"identifier": "C", "content": "$${{qvB} \\over m}... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264161/exam_images/dxv7tcthrvfo2xmv1kwt.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 11th January Evening Slot Physics - Magnetic Effect of Current Question 149 English Explanation">
... | mcq | jee-main-2019-online-11th-january-evening-slot | 11,956 |
OYiLvoW9ryQMdU4T8VOf2 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle of mass m and charge q is in an electric and magnetic field given by
<br/>$$\overrightarrow E = 2\widehat i + 3\widehat j;\,\,\,\overrightarrow B = 4\widehat j + 6\widehat k.$$
<br/><br/>The charged particle is shifted from he origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the ... | [{"identifier": "A", "content": "(2.5) q"}, {"identifier": "B", "content": "(0.35) q"}, {"identifier": "C", "content": "(0.15) q"}, {"identifier": "D", "content": "5 q"}] | ["D"] | null | $${\overrightarrow F _{net}} = q\overrightarrow E + q\left( {\overrightarrow v \times \overrightarrow B } \right)$$
<br><br>$$ = \left( {2q\widehat i + 3q\widehat j} \right) + q\left( {\overrightarrow v \times \overrightarrow B } \right)$$
<br><br>$$W = {\overrightarrow F _{net}}.\overrightarrow S $$
<br><br>$$=$$ 2... | mcq | jee-main-2019-online-11th-january-evening-slot | 11,957 |
lAxukhrRP7yjilTrpanlb | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A proton and an $$\alpha $$-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii r<sub>p</sub> : r<sub>$$\alpha $$</sub> of the ... | [{"identifier": "A", "content": "$$1:\\sqrt 3 $$"}, {"identifier": "B", "content": "1 : 3"}, {"identifier": "C", "content": "$$1:\\sqrt 2 $$"}, {"identifier": "D", "content": "1 : 2"}] | ["C"] | null | KE = q$$\Delta $$V
<br><br>r = $${{\sqrt {2mq\Delta V} } \over {qB}}$$
<br><br>r $$ \propto $$ $$\sqrt {{m \over q}} $$
<br><br>$${{{r_p}} \over {{r_ \propto }}}$$ = $${1 \over {\sqrt 2 }}$$ | mcq | jee-main-2019-online-12th-january-morning-slot | 11,958 |
xWqgc29lzk7NdmzBN618hoxe66ijvznewue | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A proton, an electron, and a Helium nucleus,
have the same energy. They are in circular
orbits in a plane due to magnetic field
perpendicualr to the plane. Let r<sub>p</sub>, r<sub>e</sub> and r<sub>He</sub> be
their respective radii, then | [{"identifier": "A", "content": "r<sub>e</sub> < r<sub>p</sub> < r<sub>He</sub>"}, {"identifier": "B", "content": "r<sub>e </sub>< r<sub>p </sub>= r<sub>He</sub>"}, {"identifier": "C", "content": "r<sub>e</sub> > r<sub>p</sub> > r<sub>He</sub>"}, {"identifier": "D", "content": "r<sub>e</sub> > r<sub>p... | ["B"] | null | $$r = {{mv} \over {qB}} = {{\sqrt {2mK} } \over {qB}}$$<br><br>
$${r_{He}} = {r_p} > {r_e}$$ | mcq | jee-main-2019-online-10th-april-morning-slot | 11,959 |
kUXhT9NQy8v4C09UvD3rsa0w2w9jx7gofnj | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $$\overrightarrow B = \left( {1.5 \times {{10}^{ - 3}}T} \right)\widehat k$$
at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is
detected at the point Q on a screen placed 8 cm away fr... | [{"identifier": "A", "content": "2.25 cm"}, {"identifier": "B", "content": "12.87 cm"}, {"identifier": "C", "content": "1.22 cm "}, {"identifier": "D", "content": "11.65 cm"}] | ["B"] | null | We know, R = $${{mv} \over {qB}}$$
<br><br>= $${{\sqrt {2mK} } \over {qB}}$$
<br><br>= $${{\sqrt {2 \times 9.1 \times {{10}^{ - 31}} \times 100 \times 1.6 \times {{10}^{ - 19}}} } \over {1.6 \times {{10}^{ - 19}} \times 1.5 \times {{10}^{ - 3}}}}$$
<br><br>= $${\sqrt 5 }$$ cm
<picture><source media="(max-width: 320px)... | mcq | jee-main-2019-online-12th-april-evening-slot | 11,960 |
P3IG6oQEjh1clZLcPYjgy2xukfroqfgp | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | An electron is moving along +x direction with a velocity of 6 $$ \times $$ 10<sup>6</sup>
ms<sup>–1</sup>. It enters a region of uniform
electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic
field set up in this region such that the electron keeps moving along the x direct... | [{"identifier": "A", "content": "3 $$ \\times $$ 10<sup>\u20134</sup> T, along \u2013z direction "}, {"identifier": "B", "content": "5 $$ \\times $$ 10<sup>\u20133</sup> T, along \u2013z direction "}, {"identifier": "C", "content": "5 $$ \\times $$ 10<sup>\u20133</sup> T, along +z direction "}, {"identifier": "D", "con... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264328/exam_images/dk2z5fyc6rr4leahspjo.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Morning Slot Physics - Magnetic Effect of Current Question 115 English Explanation">... | mcq | jee-main-2020-online-6th-september-morning-slot | 11,961 |
u58TQpoeoKjvwh0SYojgy2xukfrt30bu | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle of charge q and mass m is moving with a velocity $$ - v\widehat i$$ (v $$ \ne $$ 0) towards a large screen
placed in the Y - Z plane at a distance d. If there is a magnetic field $$\overrightarrow B = {B_0}\widehat k$$
, the maximum value of v
for which the particle will not hit the screen is : | [{"identifier": "A", "content": "$${{2qd{B_0}} \\over m}$$"}, {"identifier": "B", "content": "$${{qd{B_0}} \\over {3m}}$$"}, {"identifier": "C", "content": "$${{qd{B_0}} \\over {2m}}$$"}, {"identifier": "D", "content": "$${{qd{B_0}} \\over {m}}$$"}] | ["D"] | null | In uniform magnetic field particle moves in a circular path, if the radius of the circular path is 'd', particle will
not hit the screen.
<br><br>r = $${{mv} \over {q{B_0}}}$$
<br><br>To not collide, r < d
<br><br>$$ \Rightarrow $$ $${{mv} \over {q{B_0}}}$$ < d
<br><br>$$ \Rightarrow $$ v < $${{q{B_0}d} \over ... | mcq | jee-main-2020-online-6th-september-morning-slot | 11,962 |
V46x9roylASfAQC16ujgy2xukexw7kh8 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | The figure shows a region of length ‘l’ with a
uniform magnetic field of 0.3 T in it and a
proton entering the region with velocity 4 $$ \times $$ 10<sup>5</sup>
ms<sup>–1</sup> making an angle 60<sup>o</sup> with the field. If the
proton completes 10 revolution by the time it
cross the region shown, ‘l’ is close to <b... | [{"identifier": "A", "content": "0.22 m"}, {"identifier": "B", "content": "0.11 m"}, {"identifier": "C", "content": "0.88 m"}, {"identifier": "D", "content": "0.44 m"}] | ["D"] | null | $$l$$ = 10 × pitch
<br><br>= 10 $$ \times $$ vcos60<sup>o</sup> $$ \times $$ $${{2\pi m} \over {qB}}$$
<br><br>= 10 $$ \times $$ v $$ \times $$ $${1 \over 2}$$ $$ \times $$ $${{2\pi m} \over {qB}}$$
<br><br>= $${{10 \times 4 \times {{10}^5} \times 3.14 \times 1.67 \times {{10}^{ - 27}}} \over {1.6 \times {{10}^{ - 19}}... | mcq | jee-main-2020-online-2nd-september-evening-slot | 11,963 |
Sof0CpNW0oYg8v0zHSjgy2xukev3chc8 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A beam of protons with speed 4 × 10<sup>5</sup> ms<sup>–1</sup>
enters a uniform magnetic field of 0.3 T at an
angle of 60° to the magnetic field. The pitch of
the resulting helical path of protons is close to :
<br/>(Mass of the proton = 1.67 $$ \times $$ 10<sup>–27</sup> kg, charge
<br/>of the proton = 1.69 $$ \times... | [{"identifier": "A", "content": "2 cm"}, {"identifier": "B", "content": "12 cm"}, {"identifier": "C", "content": "5 cm"}, {"identifier": "D", "content": "4 cm"}] | ["D"] | null | Pitch = $$\frac{2\pi m}{qB} $$ vcos$$\theta $$
<br><br>= $${{2\left( {3.14} \right)\left( {1.67 \times {{10}^{ - 27}}} \right) \times 4 \times {{10}^5} \times \cos 60} \over {\left( {1.69 \times {{10}^{ - 19}}} \right)\left( {0.3} \right)}}$$
<br><br>= 0.04 m = 4 cm | mcq | jee-main-2020-online-2nd-september-morning-slot | 11,964 |
HAw7elx2SfCdIOdGgZ7k9k2k5ifgabe | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A charged particle of mass 'm' and charge 'q'
moving under the influence of uniform electric
field $$E\overrightarrow i $$
and a uniform magnetic field $$B\overrightarrow k $$
follows a trajectory from point P to Q as shown
in figure. The velocities at P and Q are
respectively, $$v\overrightarrow i $$ and $$ - 2v\overr... | [{"identifier": "A", "content": "(A), (B), (C), (D)"}, {"identifier": "B", "content": "(A), (B), (C)"}, {"identifier": "C", "content": "(A), (C), (D)"}, {"identifier": "D", "content": "(B), (C), (D)"}] | ["B"] | null | For the particle moving from point P to point Q,
<br><br>W<sub>Electric field</sub> + W<sub>Magnetic field</sub> = $$\Delta $$KE
<br><br>$$ \Rightarrow $$ qE(2$$a$$) + 0 = $${1 \over 2}m\left[ {{{\left( {2v} \right)}^2} - {v^2}} \right]$$
<br><br>$$ \Rightarrow $$ 2qE$$a$$ = $${3 \over 2}m{v^2}$$
<br><br>$$ \Rightarrow... | mcq | jee-main-2020-online-9th-january-morning-slot | 11,965 |
lyPUniC3ncJ9t0zHgM7k9k2k5gv6z8m | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | Photon with kinetic energy of 1MeV moves
from south to north. It gets an acceleration of
10<sup>12</sup> m/s<sup>2</sup> by an applied magnetic field (west to
east). The value of magnetic field : (Rest mass
of proton is 1.6 × 10<sup>–27</sup> kg) : | [{"identifier": "A", "content": "0.71mT"}, {"identifier": "B", "content": "7.1mT"}, {"identifier": "C", "content": "0.071mT"}, {"identifier": "D", "content": "71mT"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265628/exam_images/l25ezovimqa8tuewplkj.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Morning Slot Physics - Magnetic Effect of Current Question 131 English Explanation">
<... | mcq | jee-main-2020-online-8th-january-morning-slot | 11,966 |
VPKVoc6rAwW1VD5guH7k9k2k5f5pv7d | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A particle of mass m and charge q has an initial velocity $$\overrightarrow v = {v_0}\widehat j$$
. If an electric field $$\overrightarrow E = {E_0}\widehat i$$
and
magnetic field $$\overrightarrow B = {B_0}\widehat i$$
act on the particle, its speed will double after a time: | [{"identifier": "A", "content": "$${{3m{v_0}} \\over {q{E_0}}}$$"}, {"identifier": "B", "content": "$${{\\sqrt 2 m{v_0}} \\over {q{E_0}}}$$"}, {"identifier": "C", "content": "$${{\\sqrt 3 m{v_0}} \\over {q{E_0}}}$$"}, {"identifier": "D", "content": "$${{2m{v_0}} \\over {q{E_0}}}$$"}] | ["C"] | null | Electric field will increase the speed of particle in x direction.
<br><br>F<sub>x</sub> = qE
<br><br>$$ \therefore $$ a = $${{qE} \over m}$$
<br><br>Also v<sub>x</sub> = at = $${{qE} \over m}$$t
<br><br>$$v_x^2 + v_y^2 = {v^2}$$
<br><br>$$ \Rightarrow $$ $$v_x^2 + v_0^2 = {\left( {2{v_0}} \right)^2}$$
<br><br>$$ \Righ... | mcq | jee-main-2020-online-7th-january-evening-slot | 11,967 |
PA8JFkDL20IZ471iR17k9k2k5kvsfoc | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | An electron gun is placed inside a long solenoid
of radius R on its axis. The solenoid has n
turns/length and carries a current I. The
electron gun shoots an electron along the radius
of the solenoid with speed v. If the electron
does not hit the surface of the solenoid,
maximum possible value of v is (all symbols
have... | [{"identifier": "A", "content": "$${{e{\\mu _0}nIR} \\over {4m}}$$"}, {"identifier": "B", "content": "$${{e{\\mu _0}nIR} \\over m}$$"}, {"identifier": "C", "content": "$${{e{\\mu _0}nIR} \\over {2m}}$$"}, {"identifier": "D", "content": "$${{2e{\\mu _0}nIR} \\over m}$$"}] | ["C"] | null | B = $$\mu $$<sub>0</sub>nI
<br><br>$${{m{V_{\max }}} \over {qB}} = {R \over 2}$$
<br><br>V<sub>max</sub> = $${{qBR} \over {2m}}$$
<br><br>= $${{qR{\mu _0}nI} \over {2m}}$$ | mcq | jee-main-2020-online-9th-january-evening-slot | 11,968 |
RfQ4e49iMRXffj5wIf1klrwuhzn | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio. | [{"identifier": "A", "content": "2 : 1 : 1 and 4 : 2 : 1"}, {"identifier": "B", "content": "4 : 2 : 1 and 2 : 1 : 1"}, {"identifier": "C", "content": "1 : 2 : 4 and 2 : 1 : 1"}, {"identifier": "D", "content": "1 : 2 : 4 and 1 : 1 : 2"}] | ["A"] | null | F = qvB = q$${p \over m}$$B<br><br>F $$ \propto $$ $${q \over m}$$ [as p, B are const.]<br><br>$$ \therefore $$ F<sub>1</sub> : F<sub>2</sub> : F<sub>3</sub><br><br>= $${e \over m}:{e \over {2m}}:{{2e} \over {4m}}$$<br><br>= 2 : 1 : 1<br><br>And v<sub>1</sub> : v<sub>2</sub> : v<sub>3</sub><br><br>= $${p \over m}:{p \o... | mcq | jee-main-2021-online-25th-february-morning-slot | 11,969 |
kDrLrq5o2c3K8WOPuZ1kmip7mtw | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A charge Q is moving $$\overrightarrow {dl} $$ distance in the magnetic field $$\overrightarrow {B} $$. Find the value of work done by $$\overrightarrow {B} $$. | [{"identifier": "A", "content": "Zero"}, {"identifier": "B", "content": "$$-$$1"}, {"identifier": "C", "content": "Infinite"}, {"identifier": "D", "content": "1"}] | ["A"] | null | We know,<br><br>$$\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)$$<br><br>$$ \therefore $$ $$\overrightarrow F \bot \overrightarrow v $$ and $$\overrightarrow F \bot \overrightarrow B $$<br><br>Power (p) $$ = {{dw} \over {dt}}$$<br><br>$$ = {{\overrightarrow F .\,\overrightarrow {... | mcq | jee-main-2021-online-16th-march-evening-shift | 11,970 |
D0jAySzWBvwUwcOQpr1kmlwcext | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A proton and an $$\alpha$$-particle, having kinetic energies K<sub>p</sub> and K<sub>$$\alpha$$</sub> respectively, enter into a magnetic field at right angles.<br/><br/>The ratio of the radii of trajectory of proton to that of $$\alpha$$-particle is 2 : 1. The ratio of K<sub>p</sub> : K<sub>$$\alpha$$</sub> is : | [{"identifier": "A", "content": "8 : 1"}, {"identifier": "B", "content": "4 : 1"}, {"identifier": "C", "content": "1 : 8"}, {"identifier": "D", "content": "1 : 4"}] | ["B"] | null | Radius, $$r = {{mv} \over {qB}} = {{\sqrt {2mK} } \over {qB}}$$<br><br>$$ \Rightarrow K = {{{r^2}{q^2}{B^2}} \over {2m}}$$<br><br>$$ \therefore $$ $${{{K_p}} \over {{K_\alpha }}} = {\left( {{{{r_p}} \over {{r_\alpha }}}} \right)^2} \times {\left( {{{{q_p}} \over {{q_\alpha }}}} \right)^2} \times {{{m_\alpha }} \over {{... | mcq | jee-main-2021-online-18th-march-evening-shift | 11,971 |
FHjoZQLTmfNqRQWwKq1krpl002t | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r<sub>d</sub> and r<sub>$$\alpha$$</sub> be their respective radii of circular path. The value of $${{{r_d}} \over {{r_\alpha }}}$$ is equal to : | [{"identifier": "A", "content": "1"}, {"identifier": "B", "content": "2"}, {"identifier": "C", "content": "$$\\sqrt 2 $$"}, {"identifier": "D", "content": "$${1 \\over {\\sqrt 2 }}$$"}] | ["C"] | null | Given, kinetic energy of $$\alpha$$-particle (K<sub>$$\alpha$$</sub>) = kinetic energy of deuteron (K<sub>d</sub>)<br/><br/>Since, kinetic energy, K = $${1 \over 2}$$ mv<sup>2</sup><br/><br/>$$\Rightarrow$$ mv<sup>2</sup> = 2K $$\Rightarrow$$ v<sup>2</sup> = $${{2K} \over m}$$<br/><br/>$$\Rightarrow$$ v = $$\sqrt {{{2K... | mcq | jee-main-2021-online-20th-july-morning-shift | 11,972 |
1l547812a | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :</p> | [{"identifier": "A", "content": "1 : 1"}, {"identifier": "B", "content": "1 : 2"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "1 : 4"}] | ["C"] | null | <p>$$R = {{mv} \over {Bq}} = {{\sqrt {2mK} } \over {Bq}}$$</p>
<p>$$ \Rightarrow R \propto \sqrt K $$</p>
<p>$$\Rightarrow$$ ratio = 2 : 1</p> | mcq | jee-main-2022-online-29th-june-morning-shift | 11,975 |
1l54v8asd | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>Given below are two statements :</p>
<p><b>Statement I</b> : The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.</p>
<p><b>Statement II </b>: The electric force accelerates the positi... | [{"identifier": "A", "content": "Both Statement I and Statement II are correct."}, {"identifier": "B", "content": "Both Statement I and Statement II are incorrect."}, {"identifier": "C", "content": "Statement I is correct but Statement II is incorrect."}, {"identifier": "D", "content": "Statement I is incorrect but Sta... | ["C"] | null | <p>Electric field accelerates the particle in the direction of field $$\left( {\overrightarrow F = q\overrightarrow E = m\overrightarrow a } \right)$$ and magnetic field accelerates the particle perpendicular to the field $$\left( {\overrightarrow F = q\overrightarrow v \times \overrightarrow B = m\overrightarrow ... | mcq | jee-main-2022-online-29th-june-evening-shift | 11,976 |
1l56v2m4k | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>Two long parallel conductors S<sub>1</sub> and S<sub>2</sub> are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).</p>
<p>A charge particle of 3$$\pi$$ coulomb is ... | [{"identifier": "A", "content": "2"}, {"identifier": "B", "content": "1"}, {"identifier": "C", "content": "3"}, {"identifier": "D", "content": "$$-$$3"}] | ["C"] | null | <p>Field at P is $$ = \left( {{{{\mu _0} \times {i_1}} \over {2\pi {r_1}}} - {{{\mu _0}{i_2}} \over {2\pi {r_2}}}} \right)\left( { - \widehat k} \right)$$</p>
<p>$$ = - \left( {{{{\mu _0}4} \over {2\pi \times 0.04}} - {{{\mu _0} \times 2} \over {2\pi \times 0.06}}} \right)\widehat k = - {{{\mu _0} \times 200} \over... | mcq | jee-main-2022-online-27th-june-evening-shift | 11,978 |
1l58bwspu | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :</p> | [{"identifier": "A", "content": "1 : 4"}, {"identifier": "B", "content": "4 : 1"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "1 : 2"}] | ["C"] | null | $R=\frac{m v}{q B}$
<br/><br/>$\frac{\mathrm{R}_\alpha}{\mathrm{R}_{\mathrm{P}}}=\frac{\mathrm{M}_\alpha}{\mathrm{M}_{\mathrm{P}}} \times \frac{\mathrm{q}_{\mathrm{P}}}{\mathrm{q}_\alpha}$
<br/><br/>$\frac{\mathrm{R}_\alpha}{\mathrm{R}_{\mathrm{P}}}=\frac{4}{1} \times \frac{1}{2}=2$ | mcq | jee-main-2022-online-26th-june-morning-shift | 11,980 |
1l5w2th4o | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :</p>
<p>(Take : e = 1.6 $$\times$$ 10<sup>$$-$$19</sup> C, m<sub>p</sub> = 1.67 $$\times$$ 10<sup>$$-$$27</sup> kg)</p> | [{"identifier": "A", "content": "7.4 MeV"}, {"identifier": "B", "content": "14.86 MeV"}, {"identifier": "C", "content": "7.4 GeV"}, {"identifier": "D", "content": "704 GeV"}] | ["A"] | null | <p>Given,</p>
<p>$$f = 10 \times {10^6}$$ Hz</p>
<p>$$r = 0.6$$ m</p>
<p>Charge on proton (q) = e</p>
<p>We know,</p>
<p>Radius $$(r) = {{mv} \over {qB}}$$</p>
<p>$$ = {{\sqrt {2mk} } \over {eB}}$$ ..... (1)</p>
<p>Also, we know,</p>
<p>Cyclotron oscillation frequency should be equal to the pendulum evolution frequency... | mcq | jee-main-2022-online-30th-june-morning-shift | 11,981 |
jaoe38c1lsc32bux | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\overrightarrow{\mathrm{E}}$$ and $$\overrightarrow{\mathrm{B}}$$ represent the electric and magnetic fields respectively, then the region of space may have :</p>
<p>(A) $$\mathrm{E}=0, \mathrm{~B}=0$$<... | [{"identifier": "A", "content": "(A), (B) and (C) only"}, {"identifier": "B", "content": "(A), (C) and (D) only"}, {"identifier": "C", "content": "(A), (B) and (D) only"}, {"identifier": "D", "content": "(B), (C) and (D) only"}] | ["C"] | null | <p>Net force on particle must be zero i.e.
$$\mathrm{q} \overrightarrow{\mathrm{E}}+\mathrm{q} \overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}}=0$$</p>
<p>Possible cases are</p>
<p>(i) $$\overrightarrow{\mathrm{E}} \& \overrightarrow{\mathrm{B}}=0$$</p>
<p>(ii) $$\overrightarrow{\mathrm{V}} \times \overri... | mcq | jee-main-2024-online-27th-january-morning-shift | 11,983 |
jaoe38c1lse6qgul | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>An electron moves through a uniform magnetic field $$\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$$. At a particular instant of time, the velocity of electron is $$\vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$$. If the magnetic force acting on electron is $$\vec{F}=5 e \hat{k} N$$, where $$e$$ is the charge of electr... | [] | null | 5 | <p>$$\begin{aligned}
& \overrightarrow{\mathrm{F}}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& 5 \mathrm{e} \hat{\mathrm{k}}=\mathrm{e}(3 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}) \times\left(\mathrm{B}_0 \hat{\mathrm{i}}+2 \mathrm{~B}_0 \hat{\mathrm{j}}\right) \\
& 5 \mathrm{e} \hat{\mat... | integer | jee-main-2024-online-31st-january-morning-shift | 11,984 |
jaoe38c1lsfm35m3 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $$R_1$$ and $$R_2$$ respectively. The mass ratio of $$X$$ and $$Y$$ is :</p> | [{"identifier": "A", "content": "$$\\left(\\frac{R_1}{R_2}\\right)$$\n"}, {"identifier": "B", "content": "$$\\left(\\frac{R_2}{R_1}\\right)$$\n"}, {"identifier": "C", "content": "$$\\left(\\frac{R_2}{R_1}\\right)^2$$\n"}, {"identifier": "D", "content": "$$\\left(\\frac{R_1}{R_2}\\right)^2$$"}] | ["D"] | null | <p>$$\begin{aligned}
& \mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\mathrm{p}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mqV}}}{\mathrm{qB}} \\
& \mathrm{R} \propto \sqrt{\mathrm{m}} \\
& \mathrm{m} \propto \mathrm{R}^2 \\
& \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\left(\f... | mcq | jee-main-2024-online-29th-january-evening-shift | 11,985 |
jaoe38c1lsfmddke | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A charge of $$4.0 \mu \mathrm{C}$$ is moving with a velocity of $$4.0 \times 10^6 \mathrm{~ms}^{-1}$$ along the positive $$y$$ axis under a magnetic field $$\vec{B}$$ of strength $$(2 \hat{k}) \mathrm{T}$$. The force acting on the charge is $$x \hat{i} N$$. The value of $$x$$ is __________.</p> | [] | null | 32 | <p>$$\begin{aligned}
\mathrm{q} & =4 \mu \mathrm{C}, \overrightarrow{\mathrm{v}}=4 \times 10^6 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s} \\
\overrightarrow{\mathrm{B}} & =2 \hat{\mathrm{k} T} \\
\overrightarrow{\mathrm{F}} & =\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& =4 \times 10^{-... | integer | jee-main-2024-online-29th-january-evening-shift | 11,986 |
luxwcs49 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A proton and a deutron $$(q=+\mathrm{e}, m=2.0 \mathrm{u})$$ having same kinetic energies enter a region of uniform magnetic field $$\vec{B}$$, moving perpendicular to $$\vec{B}$$. The ratio of the radius $$r_d$$ of deutron path to the radius $$r_p$$ of the proton path is:</p> | [{"identifier": "A", "content": "$$1: 2$$\n"}, {"identifier": "B", "content": "$$1: 1$$\n"}, {"identifier": "C", "content": "$$\\sqrt{2}: 1$$\n"}, {"identifier": "D", "content": "$$1: \\sqrt{2}$$"}] | ["C"] | null | <p>To solve for the ratio of the radii of deutron and proton paths in a magnetic field, we use the formula for the radius $$r$$ of the circular path of a charged particle moving perpendicular to a uniform magnetic field:</p>
<p>$$r = \frac{mv}{qB}$$</p>
<p>where:</p>
<ul>
<li>$$m$$ is the mass of the particle,</li>... | mcq | jee-main-2024-online-9th-april-evening-shift | 11,987 |
lv0vxk95 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :</p> | [{"identifier": "A", "content": "the electron will experience a force at $$45^{\\circ}$$ to the axis and execute a helical path.\n"}, {"identifier": "B", "content": "the electron will be accelerated along the axis.\n"}, {"identifier": "C", "content": "the electron path will be circular about the axis.\n"}, {"identifier... | ["D"] | null | <p>For this scenario, it's important to recall how magnetic fields influence the motion of charged particles, and the configuration of the magnetic field within a solenoid. Inside a long solenoid, the magnetic field lines run parallel to the axis of the solenoid. The strength of this field is uniform and depends on the... | mcq | jee-main-2024-online-4th-april-morning-shift | 11,988 |
lv2erkz0 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>A rod of length $$60 \mathrm{~cm}$$ rotates with a uniform angular velocity $$20 \mathrm{~rad} \mathrm{s}^{-1}$$ about its perpendicular bisector, in a uniform magnetic filed $$0.5 T$$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is __... | [] | null | 0 | <p>Both end having same potential, so potential
difference between end will be zero.</p> | integer | jee-main-2024-online-4th-april-evening-shift | 11,989 |
lv5gt3f7 | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>An electron with kinetic energy $$5 \mathrm{~eV}$$ enters a region of uniform magnetic field of 3 $$\mu \mathrm{T}$$ perpendicular to its direction. An electric field $$\mathrm{E}$$ is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, i... | [] | null | 4 | <p>To solve this problem, we first need to understand that we want the electron to move along the same path in the presence of both electric and magnetic fields. This implies that the forces due to the electric field and magnetic field must balance each other.</p>
<p>The force on an electron due to the electric field ... | integer | jee-main-2024-online-8th-april-morning-shift | 11,990 |
lv9s23vh | physics | magnetics | motion-of-charged-particle-inside-magnetic-field | <p>The electrostatic force $$\left(\vec{F_1}\right)$$ and magnetic force $$\left(\vec{F}_2\right)$$ acting on a charge $$q$$ moving with velocity $$v$$ can be written :</p> | [{"identifier": "A", "content": "$$\\vec{F}_1=q \\vec{B}, \\vec{F}_2=q(\\vec{B} \\times \\vec{v})$$"}, {"identifier": "B", "content": "$$\\vec{F}_1=q \\vec{V} \\cdot \\vec{E}, \\vec{F}_2=q(\\vec{B} \\cdot \\vec{V})$$\n"}, {"identifier": "C", "content": "$$\\vec{F}_1=q \\vec{E}, \\vec{F}_2=q(\\vec{V} \\times \\vec{B})$$... | ["C"] | null | <p>The correct expressions for the electrostatic force, $\vec{F}_1$, and the magnetic force, $\vec{F}_2$, acting on a charge $q$ moving with velocity $\vec{v}$, are given by the Lorentz force law. This law states that the total force acting on a charged particle in both an electric field and a magnetic field is the sum... | mcq | jee-main-2024-online-5th-april-evening-shift | 11,991 |
uxH4yPevE4UqwfbsYX6cZ | physics | magnetics | moving-coil-galvanometer | To know the resistance G of a galvanometer by half deflection method, a battery of emf V<sub>E</sub> and resistance R is used to deflect the galvanometer by angle $$\theta $$. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation : | [{"identifier": "A", "content": "2S (R + G) = RG"}, {"identifier": "B", "content": "S (R + G) = RG"}, {"identifier": "C", "content": "2S = G"}, {"identifier": "D", "content": "2G = S"}] | ["B"] | null | When only galvanometer G is present with the resistance R,
<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266744/exam_images/xvewjzw0dhchdlul1zhq.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2016 (Online) 9th April Morning Slot Physi... | mcq | jee-main-2016-online-9th-april-morning-slot | 11,992 |
i8pSsyXVoRGZM78gF6zAq | physics | magnetics | moving-coil-galvanometer | A moving coil galvanometer has a coil with
175 turns and area 1 cm<sup>2</sup>. It uses a torsion band
of torsion constant 10<sup>–6</sup> N-m/rad. The coil is
placed in a maganetic field B parallel to its
plane. The coil deflects by 1° for a current of
1 mA. The value of B (in Tesla) is
approximately :- | [{"identifier": "A", "content": "10<sup>\u20134</sup>"}, {"identifier": "B", "content": "10<sup>\u20132</sup>"}, {"identifier": "C", "content": "10<sup>\u20131</sup>"}, {"identifier": "D", "content": "10<sup>\u20133</sup>"}] | ["D"] | null | NIAB = KQ<br><br>
175 × 1 × 10<sup>–3</sup> × 1 × 10<sup>–4</sup> × B = $${{{{10}^{ - 6}} \times \pi } \over {180}}$$<br><br>
$$ \Rightarrow B = {\pi \over {180}} \times {{10} \over {175}} \approx 9.97 \times {10^{ - 4}}\,T$$<br><br>
$$ \Rightarrow $$ B = 10<sup>–3</sup> T | mcq | jee-main-2019-online-9th-april-evening-slot | 11,993 |
QiSWUeEsoD2u36EhIHjgy2xukf3w1q14 | physics | magnetics | moving-coil-galvanometer | A galvanometer coil has 500 turns and each turn has an average area of 3 $$ \times $$ 10<sup>–4</sup> m<sup>2</sup>
. If a torque of
1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing
through it, the strength of the field (in T) is ______. | [] | null | 20 | Given N = 500
<br><br>A = 3 $$ \times $$ 10<sup>–4</sup> m<sup>2</sup>
<br><br>$$\tau $$ = 1.5 Nm
<br><br>i = 0.5 A
<br><br>We know, $$\tau = BINA\,sin\theta $$<br><br>$$1.5 = B \times 0.5 \times 500 \times 3 \times {10^{ - 4}}$$<br><br>$$B = {{10000} \over {500}} = 20$$ Tesla | integer | jee-main-2020-online-3rd-september-evening-slot | 11,994 |
1l6ma6x90 | physics | magnetics | moving-coil-galvanometer | <p>The current sensitivity of a galvanometer can be increased by :</p>
<p>(A) decreasing the number of turns</p>
<p>(B) increasing the magnetic field</p>
<p>(C) decreasing the area of the coil</p>
<p>(D) decreasing the torsional constant of the spring</p>
<p>Choose the most appropriate answer from the options given bel... | [{"identifier": "A", "content": "(B) and (C) only"}, {"identifier": "B", "content": "(C) and (D) only"}, {"identifier": "C", "content": "(A) and (C) only"}, {"identifier": "D", "content": "(B) and (D) only"}] | ["D"] | null | <p>$$NiAB = k\theta $$</p>
<p>$$ \Rightarrow {\theta \over i} = {{NAB} \over k}$$</p>
<p>$$\Rightarrow$$ Sensitivity increases if $$B \uparrow $$ and $$k \downarrow $$</p> | mcq | jee-main-2022-online-28th-july-morning-shift | 11,995 |
lsanefm9 | physics | magnetics | moving-coil-galvanometer | A moving coil galvanometer has 100 turns and each turn has an area of $2.0 \mathrm{~cm}^2$. The magnetic field produced by the magnet is $0.01 \mathrm{~T}$ and the deflection in the coil is 0.05 radian when a current of $10 \mathrm{~mA}$ is passed through it. The torsional constant of the suspension wire is $x \times 1... | [] | null | 4 | $\begin{aligned} & \tau=\text { BINAsin } \phi \\\\ & \mathrm{C} \theta=\text { BINAsin } 90^{\circ} \\\\ & \mathrm{C}=\frac{\mathrm{BINA}}{\theta}=\frac{0.01 \times 10 \times 10^{-3} \times 100 \times 2 \times 10^{-4}}{0.05} \\\\ & =4 \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad} . \\\\ & \mathrm{x}=4\end{align... | integer | jee-main-2024-online-1st-february-evening-shift | 11,996 |
LRr2aKrWHi1D7pDg | physics | motion-in-a-plane | projectile-motion | A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an
angle of $$30^\circ $$ with the horizontal. How far from the throwing point will the ball be at the height
of 10 m from the ground?
$$\left[ {g = 10m/{s^2},\sin 30^\circ = {1 \over 2},\cos 30^\circ = {{\sqrt 3 } \over 2}} \ri... | [{"identifier": "A", "content": "5.20 m"}, {"identifier": "B", "content": "4.33 m"}, {"identifier": "C", "content": "2.60 m"}, {"identifier": "D", "content": "8.66 m"}] | ["D"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266471/exam_images/mqfmaxqw4xrpjhfj6rtf.webp" loading="lazy" alt="AIEEE 2003 Physics - Motion in a Plane Question 73 English Explanation">
<br><br>From the figure it is clear that maximum horizontal range
<br><br>$$R = {{{u^2}\sin 2... | mcq | aieee-2003 | 11,997 |
RGEl2z5XwI22hTpF | physics | motion-in-a-plane | projectile-motion | A projectile can have the same range 'R' for two angles of projection. If T<sub>1</sub> and T<sub>2</sub> be the time
of flights in the two cases, then the product of the two time of flights is directly proportional to | [{"identifier": "A", "content": "R"}, {"identifier": "B", "content": "$${1 \\over R}$$"}, {"identifier": "C", "content": "$${1 \\over {{R^2}}}$$"}, {"identifier": "D", "content": "$${R^2}$$"}] | ["A"] | null | <br><br>Range is same for angle of projection $$\theta ,$$ and $${90^ \circ } - \theta $$
<br><br>$${T_1} = {{2u\sin \theta } \over g},\,\,{T_2} = {{2u\cos \theta } \over g}$$
<br><br>$${T_1}{T_2} =$$ $${{4{u^2}\sin \theta \cos \theta } \over {{g^2}}}$$
<br><br>= $${2 \over g} \times \left( {{{{u^2}\sin 2\theta } \ove... | mcq | aieee-2004 | 11,998 |
gEIilE53zPLVu7ub | physics | motion-in-a-plane | projectile-motion | A ball is thrown from a point with a speed ν<sub>0</sub> at an angle of projection θ. From the same point
and at the same instant person starts running with a constant speed $${{{v_0}} \over 2}$$ to catch the ball.
Will the person be able to catch the ball? If yes, what should be the angle of projection θ? | [{"identifier": "A", "content": "No"}, {"identifier": "B", "content": "Yes, $$30^\\circ $$"}, {"identifier": "C", "content": "Yes, $$60^\\circ $$"}, {"identifier": "D", "content": "Yes, $$45^\\circ $$"}] | ["C"] | null | Yes, the person can catch the ball when horizontal velocity is equal to the horizontal component of ball's velocity, the motion of ball will be only in vertical direction with respect to person for that,
<br><br>$${{{v_0}} \over 2} = {v_0}\cos \theta \,\,\,\,$$
<br><br>or $$\cos \theta = {1 \over 2}$$
<br><br>$$ \Ri... | mcq | aieee-2004 | 11,999 |
c0mxFZH47FebQVdS | physics | motion-in-a-plane | projectile-motion | A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a constant. The general equation for its path is | [{"identifier": "A", "content": "y = x<sup>2</sup> + constant"}, {"identifier": "B", "content": "y<sup>2</sup> = x + constant"}, {"identifier": "C", "content": "xy = constant"}, {"identifier": "D", "content": "y<sup>2</sup> = x<sup>2</sup> + constant"}] | ["D"] | null | $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$ ........(1)
<br><br>Also $$\overrightarrow v = {v_x}\widehat i + {v_y}\widehat j$$
<br><br>$$\overrightarrow v = {{dx} \over {dt}}\widehat i + {{dy} \over {dt}}\widehat j$$ ........(2)
<br><br>Equating (1) and (2), we get
<br><br> $${{dx} \over {dt}}... | mcq | aieee-2010 | 12,000 |
MELyuSXzxqi9f8q1 | physics | motion-in-a-plane | projectile-motion | A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the
fountain is v, the total area around the fountain that gets wet is : | [{"identifier": "A", "content": "$$\\pi {{{v^4}} \\over {{g^2}}}$$"}, {"identifier": "B", "content": "$${\\pi \\over 2}{{{v^4}} \\over {{g^2}}}$$"}, {"identifier": "C", "content": "$$\\pi {{{v^2}} \\over {{g^2}}}$$"}, {"identifier": "D", "content": "$$\\pi {{{v^2}} \\over g}$$"}] | ["A"] | null | Maximum range of water coming out of fountain,
<br><br>$${R_{\max }} = {{{v^2}\sin 2\theta } \over g} = {{{v^2}\sin {{90}^ \circ }} \over g} = {{{v^2}} \over g}$$
<br><br>Total area around fountain,
<br><br>$$A = \pi R_{\max }^2\,\, = \,\,\pi {{{v^4}} \over {{g^2}}}$$ | mcq | aieee-2011 | 12,001 |
haPdUvKfscDSHeJt | physics | motion-in-a-plane | projectile-motion | A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy
can throw the same stone up to will be | [{"identifier": "A", "content": "$$20\\sqrt 2 $$ m"}, {"identifier": "B", "content": "10 m"}, {"identifier": "C", "content": "$$10\\sqrt 2 $$ m"}, {"identifier": "D", "content": "20 m"}] | ["D"] | null | We know, $$R = {{{u^2}{{\sin }2}\theta } \over g}$$ and $$H = {{{u^2}{{\sin }^2}\theta } \over {2g}};$$
<br><br>$${H_{\max }}\,\,$$ is possible when $$\theta = 90$$$$^\circ $$
<br><br>$${H_{\max }} = {{{u^2}} \over {2g}} = 10 \Rightarrow {u^2} = 10g \times 2$$
<br><br>As $$R = {{{u^2}\sin 2\theta } \over g}$$
<br><b... | mcq | aieee-2012 | 12,002 |
xyWMmXYRgE7jKZJV | physics | motion-in-a-plane | projectile-motion | A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\widehat j}$$ is along the
vertical. If g = 10 m/s<sup>2</sup>, the equation of its trajectory is: | [{"identifier": "A", "content": "y = x - 5x<sup>2</sup>"}, {"identifier": "B", "content": "y = 2x - 5x<sup>2</sup>"}, {"identifier": "C", "content": "4y = 2x - 5x<sup>2</sup>"}, {"identifier": "D", "content": "4y = 2x - 25x<sup>2</sup>"}] | ["B"] | null | $$\overrightarrow u = \widehat i + 2\widehat j = {u_x}\widehat i + {u_y}\widehat j$$
<br><br>$$ \Rightarrow u\cos \theta = 1,u\sin \theta = 2$$
<br><br> Also $$x = {u_x}t$$ and
<br><br>$$y = {u_y}t - {1 \over 2}g{t^2}$$
<br><br>$$ \Rightarrow $$ $$y = x\tan \theta - {1 \over 2}{{g{x^2}} \over {u_x^2}}$$
<br><br>$... | mcq | jee-main-2013-offline | 12,003 |
3kApqFurJe6TMWclaiRfv | physics | motion-in-a-plane | projectile-motion | Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -
| [{"identifier": "A", "content": "1 : 16"}, {"identifier": "B", "content": "1 : 8"}, {"identifier": "C", "content": "1 : 2"}, {"identifier": "D", "content": "1 : 4"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267695/exam_images/pvgdnxuydh0h4di9i7xl.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 10th January Morning Slot Physics - Motion in a Plane Question 61 English Explanation">
<br><br>... | mcq | jee-main-2019-online-10th-january-morning-slot | 12,004 |
YA292aAKlwZQceD35P3rsa0w2w9jwzkieb8 | physics | motion-in-a-plane | projectile-motion | A plane is inclined at an angle $$\alpha $$ = 30° with respect to the horizontal. A particle is projected with a speed u =
2 ms<sup>–1</sup>
, from the base of the plane, making an angle $$\theta $$ = 15° with respect to the plane as shown in the figure.
the distance from the base, at which the particle hits the plane ... | [{"identifier": "A", "content": "14 cm"}, {"identifier": "B", "content": "18 cm"}, {"identifier": "C", "content": "20 cm"}, {"identifier": "D", "content": "26 cm"}] | ["C"] | null | $$T = {{2u\sin \theta } \over {g\cos \alpha }}$$<br><br>
$$R = u\cos \theta T - {1 \over 2}g\sin \alpha {T^2}$$<br><br>
$$ = {{u\cos \theta 2u\sin \theta } \over {g\cos \alpha }} - {{g\sin \alpha } \over 2}{{4{u^2}{{\sin }^2}\theta } \over {{g^2}{{\cos }^2}\alpha }}$$<br><br>
$$ = {{{u^2}{{\sin }^2}\theta } \over {g\co... | mcq | jee-main-2019-online-10th-april-evening-slot | 12,005 |
QOwadpx2jFaE8RI05e3rsa0w2w9jx3aboes | physics | motion-in-a-plane | projectile-motion | A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a
distance R from it. If t<sub>1</sub> and t<sub>2</sub> are the values of the time taken by it to hit the target in two possible ways, the
product t<sub>1</sub>t<sub>2</sub> is - | [{"identifier": "A", "content": "$${{2R} \\over g}$$"}, {"identifier": "B", "content": "$${R \\over g}$$"}, {"identifier": "C", "content": "$${R \\over {2g}}$$"}, {"identifier": "D", "content": "$${R \\over {4g}}$$"}] | ["A"] | null | Range will be same for time t<sub>1</sub> and t<sub>2</sub>, so angles of projection will be ‘$$\theta $$’ & ‘90° – $$\theta $$’<br><br>
$${t_1} = {{2u\sin \theta } \over g}{t_2} = {{2u\sin \left( {{{90}^o} - \theta } \right)} \over g}$$<br><br>
and $$R = {{{u^2}\sin 2\theta } \over g}$$<br><br>
$${t_1}{t_2} = {{4{... | mcq | jee-main-2019-online-12th-april-morning-slot | 12,006 |
1jmv4n4kvg5j2lwmpD3rsa0w2w9jx3m3zs1 | physics | motion-in-a-plane | projectile-motion | The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x<sup>2</sup>
. If it were launched at an
angle $$\theta $$<sub>0</sub> with speed v<sub>0</sub> then (g = 10 ms<sup>–2</sup>) : | [{"identifier": "A", "content": "$${\\theta _0} = {\\cos ^{ - 1}}\\left( {{1 \\over {\\sqrt 5 }}} \\right)$$ and $${v_0} = {5 \\over 3}$$ ms<sup>-1</sup>"}, {"identifier": "B", "content": "$${\\theta _0} = {\\cos ^{ - 1}}\\left( {{2 \\over {\\sqrt 5 }}} \\right)$$ and $${v_0} = {3 \\over 5}$$ ms<sup>-1</sup>"}, {"ident... | ["A"] | null | Equation of trajectory is given as<br>
y = 2x – 9x<sup>2</sup> …(A)<br><br>
Comparing with equation:<br>
$$y = x\tan \theta - {g \over {2{u^2}{{\cos }^2}\theta }}{x^2}$$ ...(B)<br><br>
We get, $$\tan \theta = 2$$<br><br>
$$ \therefore \cos \theta = {1 \over {\sqrt 5 }}$... | mcq | jee-main-2019-online-12th-april-morning-slot | 12,007 |
RS2kF4dWR8yra2pq6r3rsa0w2w9jx7pix10 | physics | motion-in-a-plane | projectile-motion | Two particles are projected from the same point with the same speed u such that they have the same range R,
but different maximum heights, h<sub>1</sub> and h<sub>2</sub>. Which of the following is correct ? | [{"identifier": "A", "content": "R<sup>2</sup>\n = h<sub>1</sub>h<sub>2</sub>"}, {"identifier": "B", "content": "R<sup>2</sup>\n = 16 h<sub>1</sub>h<sub>2</sub> "}, {"identifier": "C", "content": "R<sup>2</sup>\n = 4 h<sub>1</sub>h<sub>2</sub>"}, {"identifier": "D", "content": "R<sup>2</sup> = 2h<sub>1</sub>h<sub>2</su... | ["B"] | null | The range of two particles are same, that means angle of projections must be complementary to each other.
<br><br>So one angle = $$\theta $$ and other one is = 90<sup>o</sup> - $$\theta $$
<br><br>R = $${{{u^2}\sin 2\theta } \over g}$$ = $${{2{u^2}\sin \theta \cos \theta } \over g}$$
<br><br>$$ \therefore $$ R<sup>2</s... | mcq | jee-main-2019-online-12th-april-evening-slot | 12,008 |
RYaTrkX64f11MNp5vg1klulspsw | physics | motion-in-a-plane | projectile-motion | The trajectory of a projectile in a vertical plane is y = $$\alpha$$x $$-$$ $$\beta$$x<sup>2</sup>, where $$\alpha$$ and $$\beta$$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $$\theta$$ and the maximum height ... | [{"identifier": "A", "content": "$${\\tan ^{ - 1}}\\alpha ,{{{\\alpha ^2}} \\over {4\\beta }}$$"}, {"identifier": "B", "content": "$${\\tan ^{ - 1}}\\alpha ,{{4{\\alpha ^2}} \\over \\beta }$$"}, {"identifier": "C", "content": "$${\\tan ^{ - 1}}\\left( {{\\beta \\over \\alpha }} \\right),{{{\\alpha ^2}} \\over \\beta }... | ["A"] | null | y = $$\alpha$$x $$-$$ $$\beta$$x<sup>2</sup><br><br>comparing with trajectory equation<br><br>$$y = x\tan \theta - {1 \over 2}{{g{x^2}} \over {{u^2}{{\cos }^2}\theta }}$$<br><br>$$\tan \theta = \alpha \Rightarrow \theta = {\tan ^{ - 1}}\alpha $$<br><br>$$\beta = {1 \over 2}{g \over {{u^2}{{\cos }^2}\theta }}$$<br>... | mcq | jee-main-2021-online-26th-february-evening-slot | 12,009 |
1ktbq4cbo | physics | motion-in-a-plane | projectile-motion | A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a : | [{"identifier": "A", "content": "hyperbola"}, {"identifier": "B", "content": "parabola in the direction of motion of plane"}, {"identifier": "C", "content": "straight line vertically down the plane"}, {"identifier": "D", "content": "parabola in a direction opposite to the motion of plane"}] | ["C"] | null | <p>The correct answer is <b>Option C, a straight line vertically down the plane</b>.</p>
<p>Here's why:</p>
<ul>
<li><strong>Frame of Reference:</strong> The key to understanding projectile motion is considering the frame of reference. The observer in the plane is in a moving frame of reference. From their perspect... | mcq | jee-main-2021-online-26th-august-evening-shift | 12,010 |
1kth0r2rj | physics | motion-in-a-plane | projectile-motion | A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped? | [{"identifier": "A", "content": "$$\\sqrt {{{2gh{v^2} + 1} \\over {{h^2}}}} $$"}, {"identifier": "B", "content": "$$\\sqrt {2gh{v^2} + {h^2}} $$"}, {"identifier": "C", "content": "$$\\sqrt {{{2{v^2}h} \\over g} + {h^2}} $$"}, {"identifier": "D", "content": "$$\\sqrt {{{2gh} \\over {{v^2}}} + {h^2}} $$"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263831/exam_images/nauibi7nesllwby5lcx5.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 31st August Morning Shift Physics - Motion in a Plane Question 39 English Explanation"><br>$$R = \... | mcq | jee-main-2021-online-31st-august-morning-shift | 12,012 |
1ktmncywt | physics | motion-in-a-plane | projectile-motion | The ranges and heights for two projectiles projected with the same initial velocity at angles 42$$^\circ$$ and 48$$^\circ$$ with the horizontal are R<sub>1</sub>, R<sub>2</sub> and H<sub>1</sub>, H<sub>2</sub> respectively. Choose the correct option : | [{"identifier": "A", "content": "R<sub>1</sub> > R<sub>2</sub> and H<sub>1</sub> = H<sub>2</sub>"}, {"identifier": "B", "content": "R<sub>1</sub> = R<sub>2</sub> and H<sub>1</sub> < H<sub>2</sub>"}, {"identifier": "C", "content": "R<sub>1</sub> < R<sub>2</sub> and H<sub>1</sub> < H<sub>2</sub>"}, {"identifi... | ["B"] | null | Here, two projectiles are projected at angles 42$$^\circ$$ and 48$$^\circ$$ with same initial velocity.<br/><br/>As we know the expression of range of projectile, <br/><br/>Range $$ = {{{u^2}\sin 2\theta } \over g}$$<br/><br/>AT $$\theta$$<sub>1</sub> = 42$$^\circ$$,<br/><br/>Range, $${R_1} = {{{u^2}\sin 2(42)^\circ } ... | mcq | jee-main-2021-online-1st-september-evening-shift | 12,013 |
1l54vi0gs | physics | motion-in-a-plane | projectile-motion | <p>A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?</p> | [{"identifier": "A", "content": "25 m"}, {"identifier": "B", "content": "50 m"}, {"identifier": "C", "content": "100 m"}, {"identifier": "D", "content": "200 m"}] | ["B"] | null | <p>To determine how high a person can throw a ball given the maximum range, we need to use the principles of projectile motion in physics. The maximum range of a projectile is given by the formula:</p>
<p>$$ R = \frac{{v_0^2 \sin(2\theta)}}{g} $$</p>
<p>where:</p>
<ul>
<li>$$ R $$ is the range</li>
<li>$$ v_0 $$ i... | mcq | jee-main-2022-online-29th-june-evening-shift | 12,014 |
1l57pde0b | physics | motion-in-a-plane | projectile-motion | <p>A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms<sup>$$-$$1</sup>. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms<sup>$$-$$2</sup>).</p> | [{"identifier": "A", "content": "tan$$\\alpha$$ + 5sec$$\\alpha$$"}, {"identifier": "B", "content": "tan$$\\alpha$$ $$-$$ 5sec$$\\alpha$$"}, {"identifier": "C", "content": "2tan$$\\alpha$$ $$-$$ 5sec$$\\alpha$$"}, {"identifier": "D", "content": "2tan$$\\alpha$$ $$+$$ 5sec$$\\alpha$$"}] | ["B"] | null | At $t=0$, the motion of projectile is given as
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lb32efin/6418c902-59be-4295-b3f4-eeb0c1462490/bca5c9f0-705b-11ed-89c6-814873432a68/file-1lb32efio.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lb32efin/6418c902-59be-4295-b3... | mcq | jee-main-2022-online-27th-june-morning-shift | 12,015 |
1l58cecmx | physics | motion-in-a-plane | projectile-motion | <p>A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms<sup>$$-$$1</sup>. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $$\theta$$ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of $$\theta$$ will be ______... | [] | null | 60 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7ta5g03/68fabda1-4ee5-4380-80d5-62e1f1cd3f80/8f245930-2f95-11ed-a1d8-e368d72cfa4f/file-1l7ta5g04.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7ta5g03/68fabda1-4ee5-4380-80d5-62e1f1cd3f80/8f245930-2f95-11ed-a1d8-e368d72cfa4f/fi... | integer | jee-main-2022-online-26th-june-morning-shift | 12,016 |
1l59ltdki | physics | motion-in-a-plane | projectile-motion | <p>Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.</p>
<p>Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h<sub>1</sub> and h<sub>2</sub>... | [{"identifier": "A", "content": "Both A and R are true and R is the correct explanation of A."}, {"identifier": "B", "content": "Both A and R are true but R is NOT the correct explanation of A."}, {"identifier": "C", "content": "A is true but R is false."}, {"identifier": "D", "content": "A is false but R is true."}] | ["A"] | null | <p>When two projectiles are thrown with the same initial velocity 'u' but at complementary angles (say, $\theta$ and $(90^\circ - \theta)$) with the horizontal, they attain the same range R. The formula for the range R of a projectile is:</p>
<p>$$ R = \frac{u^2 \sin 2\theta}{g} $$</p>
<p>For complementary angles, $2... | mcq | jee-main-2022-online-25th-june-evening-shift | 12,017 |
1l5c2upa5 | physics | motion-in-a-plane | projectile-motion | <p>A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $$\theta$$ will be :</p>
<p>[use g = 10 m/s<sup>2</sup>]</p> | [{"identifier": "A", "content": "$${1 \\over 2}{\\sin ^{ - 1}}\\left( {{{5{t^2}} \\over {4R}}} \\right)$$"}, {"identifier": "B", "content": "$${1 \\over 2}{\\sin ^{ - 1}}\\left( {{{4R} \\over {5{t^2}}}} \\right)$$"}, {"identifier": "C", "content": "$${\\tan ^{ - 1}}\\left( {{{4{t^2}} \\over {5R}}} \\right)$$"}, {"ident... | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5leb42a/25a8df8a-4ab3-4e4c-a666-4c52b473ee0b/1d567320-03a7-11ed-b731-675fd498ca49/file-1l5leb42b.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5leb42a/25a8df8a-4ab3-4e4c-a666-4c52b473ee0b/1d567320-03a7-11ed-b731-675fd498ca49... | mcq | jee-main-2022-online-24th-june-morning-shift | 12,019 |
1l5w1teip | physics | motion-in-a-plane | projectile-motion | <p>At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms<sup>$$-$$2</sup>. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be :</p>
<p>(Given g = 1... | [{"identifier": "A", "content": "$$100\\widehat i - 10\\widehat j$$"}, {"identifier": "B", "content": "$$10\\widehat i - 100\\widehat j$$"}, {"identifier": "C", "content": "$$100\\widehat i$$"}, {"identifier": "D", "content": "$$ - 10\\widehat j$$"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6dnc0pm/b620b3bb-0e9e-4911-8cdc-a49bb6f101e0/5ae74fa0-1330-11ed-941a-4dd6502f33e3/file-1l6dnc0pn.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6dnc0pm/b620b3bb-0e9e-4911-8cdc-a49bb6f101e0/5ae74fa0-1330-11ed-941a-4dd6502f33e3... | mcq | jee-main-2022-online-30th-june-morning-shift | 12,020 |
1l6f59icd | physics | motion-in-a-plane | projectile-motion | <p>A ball is projected from the ground with a speed 15 ms<sup>$$-$$1</sup> at an angle $$\theta$$ with horizontal so that its range and maximum height are equal, <br/>then 'tan $$\theta$$' will be equal to :</p> | [{"identifier": "A", "content": "$${1 \\over 4}$$"}, {"identifier": "B", "content": "$${1 \\over 2}$$"}, {"identifier": "C", "content": "2"}, {"identifier": "D", "content": "4"}] | ["D"] | null | <p>To solve this problem, we will use the equations for the range and maximum height of a projectile. The range $$R$$ and maximum height $$H$$ of a projectile launched with speed $$u$$ at an angle $$\theta$$ can be expressed as follows:</p>
<p>Range:</p>
<p>$$R = \frac{u^2 \sin(2\theta)}{g}$$</p>
<p>Maximum height:<... | mcq | jee-main-2022-online-25th-july-evening-shift | 12,022 |
1l6gn91d5 | physics | motion-in-a-plane | projectile-motion | <p>Two projectiles thrown at $$30^{\circ}$$ and $$45^{\circ}$$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :</p> | [{"identifier": "A", "content": "$$1: \\sqrt{2}$$"}, {"identifier": "B", "content": "$$2: 1$$"}, {"identifier": "C", "content": "$$\\sqrt{2}: 1$$"}, {"identifier": "D", "content": "$$1: 2$$"}] | ["C"] | null | <p>To solve this problem, we need to understand the relationship between the angles of projection, the initial velocities, and the time taken to reach maximum height for each projectile.</p>
<p>The formula to calculate the time to reach the maximum height is given by:</p>
<p>
<p>$$ t = \frac{u \sin \theta}{g} $$</p>... | mcq | jee-main-2022-online-26th-july-morning-shift | 12,023 |
1l6gnevp4 | physics | motion-in-a-plane | projectile-motion | <p>If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y=5 x(1-x)$$. The $$y$$ component vector of the initial velocity is ______________ $$\hat{j}$$. ($$\mathrm{Take}$$ $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$</p> | [] | null | 5 | <p>If the initial velocity in the horizontal direction of a projectile is represented by the unit vector $$\hat{i}$$ and the equation of the trajectory is given by $$y = 5x(1 - x)$$, we need to find the $$y$$ component vector of the initial velocity. (Given: $$g = 10 \mathrm{\ m/s^2}$$)</p>
<p>The trajectory equation ... | integer | jee-main-2022-online-26th-july-morning-shift | 12,024 |
1l6i08jhz | physics | motion-in-a-plane | projectile-motion | <p>Two projectiles are thrown with same initial velocity making an angle of $$45^{\circ}$$ and $$30^{\circ}$$ with the horizontal respectively. The ratio of their respective ranges will be :</p> | [{"identifier": "A", "content": "$$1: \\sqrt{2}$$"}, {"identifier": "B", "content": "$$\\sqrt{2}: 1$$"}, {"identifier": "C", "content": "$$2: \\sqrt{3}$$"}, {"identifier": "D", "content": "$$\\sqrt{3}: 2$$"}] | ["C"] | null | <p>Here's how to determine the ratio of the ranges for the two projectiles:</p>
<p><strong>Understanding the Concepts</strong></p>
<ul>
<li><strong>Projectile Motion:</strong> Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is cal... | mcq | jee-main-2022-online-26th-july-evening-shift | 12,025 |
1l6jk4syj | physics | motion-in-a-plane | projectile-motion | <p>A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $$\frac{1}{x}$$. The value of x is _____________.</p> | [] | null | 1 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6xtoci1/bb30e765-69ec-4e05-8a17-2c210e0d791d/d57bc390-1e48-11ed-9c61-4529b721806b/file-1l6xtoci2.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6xtoci1/bb30e765-69ec-4e05-8a17-2c210e0d791d/d57bc390-1e48-11ed-9c61-4529b721806b... | integer | jee-main-2022-online-27th-july-morning-shift | 12,026 |
1l6p5woub | physics | motion-in-a-plane | projectile-motion | <p>An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of t... | [] | null | 15OR75 | $\begin{aligned} & \mathrm{R}_{\max }=\frac{\mathrm{u}^2 \sin 2\left(45^{\circ}\right)}{\mathrm{g}}=\frac{\mathrm{u}^2}{\mathrm{~g}} \\\\ & \frac{\mathrm{R}}{2}=\frac{\mathrm{u}^2}{2 \mathrm{~g}}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}} \\\\ & \sin 2 \theta=\frac{1}{2} \\\\ & 2 \theta=30^{\circ}, 150^{\circ} \\\\ ... | integer | jee-main-2022-online-29th-july-morning-shift | 12,027 |
ldo7i1br | physics | motion-in-a-plane | projectile-motion | Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is $\... | [] | null | 80 | <p>When two bodies are projected from the ground at the same speed of $40 \mathrm{~ms}^{-1}$ but at different angles, and they achieve the same range, we can derive the following:</p>
<p>Given that one projectile is launched at an angle of $60^\circ$ with respect to the horizontal, let's denote the angles of projectio... | integer | jee-main-2023-online-31st-january-evening-shift | 12,028 |
1ldofpzui | physics | motion-in-a-plane | projectile-motion | <p>A child stands on the edge of the cliff $$10 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initial speed of $$5 \mathrm{~ms}^{-1}$$. Neglecting the air resistance, the speed with which the stone hits the ground will be $$\mathrm{ms}^{-1}$$ (given, $$g=10 \mathrm{~ms}^{-2}$$ ).</p> | [{"identifier": "A", "content": "20"}, {"identifier": "B", "content": "25"}, {"identifier": "C", "content": "30"}, {"identifier": "D", "content": "15"}] | ["D"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le6y9k62/70351e9e-3f9d-4e71-8216-f71dc416f83d/59697ba0-ade3-11ed-88ce-eb0402d729eb/file-1le6y9k63.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le6y9k62/70351e9e-3f9d-4e71-8216-f71dc416f83d/59697ba0-ade3-11ed-88ce-eb0402d729eb/fi... | mcq | jee-main-2023-online-1st-february-morning-shift | 12,029 |
1ldpjmv71 | physics | motion-in-a-plane | projectile-motion | <p>The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed of projectile is $$\frac{\sqrt{3}}{2} u$$. The time of flight of the projectile is :</p> | [{"identifier": "A", "content": "$$\\frac{u}{g}$$"}, {"identifier": "B", "content": "$$\\frac{2u}{g}$$"}, {"identifier": "C", "content": "$$\\frac{u}{2g}$$"}, {"identifier": "D", "content": "$$\\frac{\\sqrt3u}{g}$$"}] | ["A"] | null | $u \cos \theta=\frac{\sqrt{3}}{2} u$
<br/><br/>$$ \Rightarrow $$ $\cos \theta=\frac{\sqrt{3}}{2}$
<br/><br/>$$ \Rightarrow $$ $\theta=30^{\circ}$
<br/><br/>Time of flight $=\frac{2 u \sin \theta}{g}=\left(\frac{u}{g}\right)$ | mcq | jee-main-2023-online-31st-january-morning-shift | 12,030 |
1ldtymbtk | physics | motion-in-a-plane | projectile-motion | <p>Two objects are projected with same velocity 'u' however at different angles $$\alpha$$ and $$\beta$$ with the horizontal. If $$\alpha+\beta=90^\circ$$, the ratio of horizontal range of the first object to the 2nd object will be :</p> | [{"identifier": "A", "content": "1 : 1"}, {"identifier": "B", "content": "2 : 1"}, {"identifier": "C", "content": "1 : 2"}, {"identifier": "D", "content": "4 : 1"}] | ["A"] | null | $$
\text {Range}=\frac{u^2 \sin 2 \theta}{g}
$$<br/><br/>
Range for projection angle " $\alpha$ "<br/><br/>
$$
\mathrm{R}_1=\frac{\mathrm{u}^2 \sin 2 \alpha}{\mathrm{g}}
$$<br/><br/>
Range for projection angle " $\beta$ "<br/><br/>
$$
\begin{aligned}
& \mathrm{R}_2=\frac{\mathrm{u}^2 \sin 2 \beta}{\mathrm{g}} \\\\
& \a... | mcq | jee-main-2023-online-25th-january-evening-shift | 12,031 |
1ldye79sy | physics | motion-in-a-plane | projectile-motion | <p>The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :</p> | [{"identifier": "A", "content": "136 m"}, {"identifier": "B", "content": "272 m"}, {"identifier": "C", "content": "68 m"}, {"identifier": "D", "content": "192 m"}] | ["B"] | null | For vertical throw,
<br/><br/>
$$
\begin{aligned}
& h=\frac{v^{2}}{2 g} \\\\
& v=\sqrt{2 g h}=\sqrt{2 g \times 136} \quad...(1)
\end{aligned}
$$
<br/><br/>
For max range, $\theta=45^{\circ}$
<br/><br/>
$R_{\max }=\frac{v^{2}}{g} \quad...(2)$
<br/><br/>
From (1) and (2)
<br/><br/>
$$
\begin{aligned}
R_{\max } & =\frac{... | mcq | jee-main-2023-online-24th-january-morning-shift | 12,032 |
1lguyit55 | physics | motion-in-a-plane | projectile-motion | <p>A projectile fired at $$30^{\circ}$$ to the ground is observed to be at same height at time $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ after projection, during its flight. The speed of projection of the projectile is ___________ $$\mathrm{m} ~\mathrm{s}^{-1}$$.</p>
<p>(Given $$g=10 \mathrm{~ms}^{-2}$$ )</p> | [] | null | 80 | <p>Given:</p>
<ol>
<li>The angle of projection $$\theta = 30^{\circ}$$.</li>
<li>The projectile is at the same height at time $$t_1 = 3 \mathrm{~s}$$ and $$t_2 = 5 \mathrm{~s}$$.</li>
<li>The acceleration due to gravity $$g = 10 \mathrm{~m/s^2}$$.</li>
</ol>
<p>We need to find the initial speed of projection, $$u$$.</p... | integer | jee-main-2023-online-11th-april-morning-shift | 12,034 |
1lgvrj2my | physics | motion-in-a-plane | projectile-motion | <p>Two projectiles are projected at $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:</p> | [{"identifier": "A", "content": "$$1: \\sqrt{3}$$"}, {"identifier": "B", "content": "$$\\sqrt{3}: 1$$"}, {"identifier": "C", "content": "1 : 3"}, {"identifier": "D", "content": "$$2: \\sqrt{3}$$"}] | ["C"] | null | <p>Let the initial speed of both projectiles be v. The maximum height attained by a projectile can be calculated using the formula:</p>
<p>$$H = \frac{v^2 \sin^2 \theta}{2g}$$</p>
<p>where H is the maximum height, v is the initial speed, θ is the angle of projection, and g is the acceleration due to gravity.</p>
<p>For... | mcq | jee-main-2023-online-10th-april-evening-shift | 12,035 |
1lgyqw4iu | physics | motion-in-a-plane | projectile-motion | <p>The trajectory of projectile, projected from the ground is given by $$y=x-\frac{x^{2}}{20}$$. Where $$x$$ and $$y$$ are measured in meter. The maximum height attained by the projectile will be.</p> | [{"identifier": "A", "content": "10 m"}, {"identifier": "B", "content": "5 m"}, {"identifier": "C", "content": "200 m"}, {"identifier": "D", "content": "10$$\\sqrt2$$ m"}] | ["B"] | null | <p>The equation of the trajectory given is $y = x - \frac{x^2}{20}$.<br/><br/> This is a parabola, and it represents the path of the projectile.</p>
<p>The maximum height of the projectile corresponds to the vertex of the parabola.<br/><br/> The x-coordinate of the vertex for a parabola given by $y = ax^2 + bx + c$ is ... | mcq | jee-main-2023-online-8th-april-evening-shift | 12,037 |
1lh01di29 | physics | motion-in-a-plane | projectile-motion | <p>Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$</p> | [{"identifier": "A", "content": "$$4: 9$$"}, {"identifier": "B", "content": "$$2: \\sqrt{3}$$"}, {"identifier": "C", "content": "$$\\sqrt{3}: 2$$"}, {"identifier": "D", "content": "$$1: 1$$"}] | ["A"] | null | <p>The range of a projectile launched with an initial velocity $v$ at an angle $\theta$ with respect to the horizontal is given by:</p>
<p>$R = \frac{v^2 \sin(2\theta)}{g}$,</p>
<p>where $g$ is the acceleration due to gravity.</p>
<p>Let's calculate the ranges of projectiles A and B:</p>
<p>For projectile A, $v = 4... | mcq | jee-main-2023-online-8th-april-morning-shift | 12,038 |
1lh24d4cw | physics | motion-in-a-plane | projectile-motion | <p>Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R</p>
<p>Assertion A : When a body is projected at an angle $$45^{\circ}$$, it's range is maximum.</p>
<p>Reason R : For maximum range, the value of $$\sin 2 \theta$$ should be equal to one.</p>
<p>In the light of the... | [{"identifier": "A", "content": "Both $$\\mathbf{A}$$ and $$\\mathbf{R}$$ are correct and $$\\mathbf{R}$$ is the correct explanation of $$\\mathbf{A}$$"}, {"identifier": "B", "content": "$$\\mathbf{A}$$ is true but $$\\mathbf{R}$$ is false"}, {"identifier": "C", "content": "$$\\mathbf{A}$$ is false but $$\\mathbf{R}$$ ... | ["A"] | null | <b>Assertion A</b>: When a body is projected at an angle of $45^{\circ}$, its range is maximum. This is true, and it's a well-established fact in physics. The maximum range of a projectile, assuming no air resistance and flat terrain, is achieved at an angle of $45^{\circ}$.
<br/><br/>
<b>Reason R</b>: For maximum rang... | mcq | jee-main-2023-online-6th-april-morning-shift | 12,039 |
jaoe38c1lsf2c9hr | physics | motion-in-a-plane | projectile-motion | <p>A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimum velocity $$u$$ with which that ball just hits the step 5 of the stairway will be $$\sqrt{x} \mathrm{~ms}^{-1}$$ where $$x=$$ __________ [use $$\mathrm{g}=10 \mathrm{... | [] | null | 2 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lt2vi4i5/d852b197-8c62-4a52-a706-71a1911dbca9/a84b2df0-d49c-11ee-8574-81dc091f6c89/file-1lt2vi4i7.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lt2vi4i5/d852b197-8c62-4a52-a706-71a1911dbca9/a84b2df0-d49c-11ee-8574-81dc091f6c89... | integer | jee-main-2024-online-29th-january-morning-shift | 12,041 |
1lsg6q118 | physics | motion-in-a-plane | projectile-motion | <p>Projectiles A and B are thrown at angles of $$45^{\circ}$$ and $$60^{\circ}$$ with vertical respectively from top of a $$400 \mathrm{~m}$$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v_A: v_B$$ is :</p>
<p>[Take $$g=10 \mathrm{~ms}^{-2}$$]</p> | [{"identifier": "A", "content": "$$1: 2$$\n"}, {"identifier": "B", "content": "$$\\sqrt{2}: 1$$\n"}, {"identifier": "C", "content": "$$1: \\sqrt{2}$$\n"}, {"identifier": "D", "content": "$$1: \\sqrt{3}$$"}] | [] | null | <p>For $$\mathrm{u}_{\mathrm{A}}$$ & $$\mathrm{u}_{\mathrm{B}}$$ time of flight and range can not be same. So above options are incorrect.</p> | mcq | jee-main-2024-online-30th-january-evening-shift | 12,042 |
lv0vxm48 | physics | motion-in-a-plane | projectile-motion | <p>The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$$.</p>
<p>The motion of the particle is :</p> | [{"identifier": "A", "content": "uniform motion along a straight line.\n"}, {"identifier": "B", "content": "non-uniformly accelerated.\n"}, {"identifier": "C", "content": "uniformly accelerated having motion along a straight line.\n"}, {"identifier": "D", "content": "uniformly accelerated having motion along a paraboli... | ["D"] | null | <p>To determine the nature of the motion of the particle given by its coordinates in the $$x$$-$$y$$ plane, we analyze the given equations for $$x$$ and $$y$$ in terms of time $$t$$:</p>
<ul>
<li>$$x = 2 + 4t$$</li>
<li>$$y = 3t + 8t^2$$</li>
</ul>
<p>Firstly, the equation for $$x$$ is of the form $$x = x_0 + vt$$... | mcq | jee-main-2024-online-4th-april-morning-shift | 12,043 |
lv3vec4o | physics | motion-in-a-plane | projectile-motion | <p>The angle of projection for a projectile to have same horizontal range and maximum height is :</p> | [{"identifier": "A", "content": "$$\\tan ^{-1}\\left(\\frac{1}{2}\\right)$$\n"}, {"identifier": "B", "content": "$$\\tan ^{-1}(2)$$\n"}, {"identifier": "C", "content": "$$\\tan ^{-1}\\left(\\frac{1}{4}\\right)$$\n"}, {"identifier": "D", "content": "$$\\tan ^{-1}(4)$$"}] | ["D"] | null | <p>To find the angle of projection for a projectile to have the same horizontal range and maximum height, we need to express both the range and the maximum height in terms of the projectile's initial velocity and the angle of projection, and then set them equal to each other.</p>
<p>The formula for the horizontal rang... | mcq | jee-main-2024-online-8th-april-evening-shift | 12,044 |
lv3xmamv | physics | motion-in-a-plane | projectile-motion | <p>A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of $$100 \mathrm{~m}$$ from the foot of the tower. A body of mass $$2 \mathrm{~M}$$ thrown at a velocity $$\frac{v}{2}$$ from the top of the tower of height $$4 \mathrm{H}$$ will touch the grou... | [] | null | 100 | <p>To solve this problem, we can use the equations of motion under uniform acceleration, separately considering the horizontal and vertical motions because the two are independent of each other.</p>
<p>First, for the body of mass $M$ thrown horizontally with velocity $v$ from a height $H$, let's analyze its motion:</p... | integer | jee-main-2024-online-8th-april-evening-shift | 12,045 |
lv9s25lo | physics | motion-in-a-plane | projectile-motion | <p>The maximum height reached by a projectile is $$64 \mathrm{~m}$$. If the initial velocity is halved, the new maximum height of the projectile is ______ $$\mathrm{m}$$.</p> | [] | null | 16 | <p>To solve this problem, we first need to understand the formula that relates the maximum height $H$ reached by a projectile to its initial velocity $v_0$ and the acceleration due to gravity $g$:
<p>$H = \frac{v_0^2 \sin^2(\theta)}{2g}$</p>
<p>where:</p>
<ul>
<li>$H$ is the maximum height,</li><br>
<li>$v_0$ is the... | integer | jee-main-2024-online-5th-april-evening-shift | 12,046 |
yCYxrhsJ1NECSxo9Tnjgy2xukfyym9zb | physics | motion-in-a-plane | rain-man-problems | When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with
speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further
increasing the speed of the car to (1 + $$\beta $$)v, this angle changes to 45<sup>o</sup>. The value of $$\beta $$ is close t... | [{"identifier": "A", "content": "0.50"}, {"identifier": "B", "content": "0.73"}, {"identifier": "C", "content": "0.37"}, {"identifier": "D", "content": "0.41"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267182/exam_images/zxewx5hnjg3pd3lifus1.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Evening Slot Physics - Motion in a Plane Question 48 English Explanation">
<br><br>t... | mcq | jee-main-2020-online-6th-september-evening-slot | 12,047 |
1l57pfsna | physics | motion-in-a-plane | rain-man-problems | <p>A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15$$\sqrt2$$ kmh<sup>$$-$$1</sup>, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :</p> | [{"identifier": "A", "content": "30 kmh<sup>$$-$$1</sup>"}, {"identifier": "B", "content": "$${{25} \\over {\\sqrt 2 }}$$ kmh<sup>$$-$$1</sup>"}, {"identifier": "C", "content": "$${{30} \\over {\\sqrt 2 }}$$ kmh<sup>$$-$$1</sup>"}, {"identifier": "D", "content": "25 kmh<sup>$$-$$1</sup>"}] | ["C"] | null | <p> <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5jqjdcz/0d73facd-c43a-40f0-a701-c8bd1ba9e4ed/5f3e5b30-02bd-11ed-95db-c3fa9a0f41ba/file-1l5jqjdd0.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5jqjdcz/0d73facd-c43a-40f0-a701-c8bd1ba9e4ed/5f3e5b30-02bd-11ed-95db-c3fa9a0f41b... | mcq | jee-main-2022-online-27th-june-morning-shift | 12,048 |
K6sHbSdpjPN2aJY5 | physics | motion-in-a-plane | relative-motion-in-two-dimension | A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity
changes to 5 m/s northwards. The average acceleration in this time is | [{"identifier": "A", "content": "$${1 \\over 2}m{s^{ - 2}}$$ towards north"}, {"identifier": "B", "content": "$${1 \\over {\\sqrt 2 }}m{s^{ - 2}}$$ towards north-east"}, {"identifier": "C", "content": "$${1 \\over {\\sqrt 2 }}m{s^{ - 2}}$$ towards north-west"}, {"identifier": "D", "content": "zero"}] | ["C"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263740/exam_images/madr99i1r8avwnbt3ne5.webp" loading="lazy" alt="AIEEE 2005 Physics - Motion in a Plane Question 70 English Explanation">
<br><br>Average acceleration
<br><br>$$ = {{change\,\,in\,\,velocioty} \over {time\,\,{\mat... | mcq | aieee-2005 | 12,049 |
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