id stringlengths 1 4 | media images listlengths 1 1 | messages stringlengths 334 2.24k |
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0 | [{"role": "user", "question": "A patient with a dislocated shoulder is put into a traction apparatus as shown in figure. The pulls $\\vec{A}$ and $\\vec{B} must combine to produce an outward traction force of 12.8 N on the patient’s arm. How large should these pulls be?Please directly answer the question and provide th... | |
1 | [{"role": "user", "question": "All of the stars of the Big Dipper may appear to be the same distance from the earth, but in fact they are very far from each other. figure shows the distances from the earth to each of these stars.The distances are given in light-years (ly), the distance that light travels in one year. ... | |
10 | [{"role": "user", "question": "A typical graph of blood velocity versus time during a single heartbeat is shown in figure. Which statement is the best interpretation of this graph?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: the acceleration of the blood i... | |
100 | [{"role": "user", "question": "A solid uniform ball rolls without slipping up a hill as shown in figure. At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff. Neglect rolling friction and assume the system’s total mechanical energy is conserved. How fast is it moving just before i... | |
1000 | [{"role": "user", "question": "A triangular wave pulse moving at 2 cm/s on a rope approached an end at which it is free to slide on a veritcal pole. What is the particle speed on the trailing edge P at the instant depicted?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D.... | |
1001 | [{"role": "user", "question": "A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm, respectively. If the tension is 10 N and the linear mass density is 4 g/m, what is the fundamental frequency?Please directly answer the question and provide ... | |
1002 | [{"role": "user", "question": "A string of linear mass density 5.0 \\times 10^{-3} kg/m is stretched under a tension of 65 N between two rigid supports 60 cm apart. If the string is vibrating in its second overtone so that the amplitude at one of its antinodes is 0.25 cm, what are the maximum transverse speed and accel... | |
1003 | [{"role": "user", "question": "An aluminium wire of cross-sectional area 10^{-6} m^2 is joined to a steel wire of the same cross-sectional area. This compound wire is stretched on a sonometer pulled by a weight of 10 kg. The total length of the compound wire between the bridges is 1.5 m of which the aluminium wire is 0... | |
1004 | [{"role": "user", "question": "A string linear mass density 0.4 g /cm is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t= 0 near an end. When will the string have the shape shown in the figure again?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g... | |
1005 | [{"role": "user", "question": "The figure shows standing wave pattern on a string of linear mass density 4.0 \\times 1n-{-2} kg/ m under a tension of 100 N. The length of the string is 2.0m. Obtain the frequency.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A... | |
1006 | [{"role": "user", "question": "The figure shows standing wave pattern on a string of linear mass density 4.0 \\times 1n-{-2} kg/ m under a tension of 100 N. The length of the string is 2.0m. Obtain the frequency.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A... | |
1007 | [{"role": "user", "question": "At t= 0,a pulse travelling from left to right at 1 cm/s is some distance from the right end as shown in figure. Determine the next time when the pulse will be at that point again.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7... | |
1008 | [{"role": "user", "question": "Mass per unit length of string-2 is nine times that of string-1. Tension in both the strings is same. A transverse wave is incident at the boundary. Part of wave is reflected in medium-1 and part is transmitted to medium-2. Determine $v_1$ / $v_2$.Please directly answer the question and p... | |
1009 | [{"role": "user", "question": "A light string is tied at one end to fixed support and to a heavy string of equal length L at the other end as shown in figure. Mass per unit length of the strings are \\mu and 9\\mu and the tension is T. Find the smallest possible values of frequencu such that point A isanode/antinode.Pl... | |
101 | [{"role": "user", "question": "A solid, uniform, spherical boulder starts from rest and rolls down a hill, as shown in as shown in figure. The top half of the hill is rough enough to cause the boulder to roll without slipping, but the lower half is covered with ice and there is no friction. What is the translational sp... | |
1010 | [{"role": "user", "question": "A metal rod of length 1 m is clamped at two points. Given that Young’s modulus of elasticity and density of aluminium areY = 1.6 \\times 10^{11} Nm^{-2} and \\rho = 2500 kgm^{-3}, respectively. Find the minimum frequency of natural longitudinal oscillation of the rod. Please directly answ... | |
1011 | [{"role": "user", "question": "A car approaching a crossing C at a speed of 20 m/s sounds a horn of frequency 500 Hz. Speed of sound in air is 330 m/s. What frequency is heard by an observer (at rest) 60 m from the crossing on the straight road which crosses car road at right angles?Please directly answer the question ... | |
1012 | [{"role": "user", "question": "A whistle of frequency 540 Hz rotates in a circle of radius 2 m at a linear speed of 30 m s /. Take speed of sound in air as 330 m/s. What is the highest frequency heard by an observer a long distance away at rest with respect to the centre of circle?Please directly answer the question an... | |
1013 | [{"role": "user", "question": "A siren emitting a sound of frequency 1000 Hz moves away from you toward a cliff at a speed of 10 m/s. What beat frequency would you hear? Take the speed of sound in air as 330 m/s.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A:... | |
1014 | [{"role": "user", "question": "A source of sound of frequency f is approaching towards a wall with speed $v_s$ . Speed of sound is v. Find the beat frequency as observed by O_2.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7 Hz B: 0.8 Hz C: 10 Hz D: 0 Hz"... | |
1015 | [{"role": "user", "question": "A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with an angular velocity of 20 rad/s in the horizontal plane. Calculate the minimum frequency heard by an observer stationed at a large distance from the whistle. (Speed of sound= 330 m/s).Pleas... | |
1016 | [{"role": "user", "question": "The water level in a vertical glass tube 1.0 m long can be adjusted to any position in the tube. A tuning fork vibrating at 660 Hz is held just over the open top end of the tube. What is the highest position of the water level will there be in resonance? Speed of sound is 330 m/s.Please d... | |
1017 | [{"role": "user", "question": "A source of sound of frequency 1000 Hz moves uniformly along a straight line with velocity 0.8 times velocity of sound. An observer is located at a distance l = 250m from this line. What is the distance of the source when he observes no change in the frequency?Please directly answer the q... | |
1018 | [{"role": "user", "question": "The air column is made to vibrate in its second overtone by a tuning fork of frequency 440 Hz. The speed of sound in air is 330 m/s. End corrections may be neglected. Let $p_0$ denotes the mean pressure at any point in the pipe, and $\\delt p_0$ the maximum amplitude of pressure variation... | |
1019 | [{"role": "user", "question": "A boat is travelling in a river along the stream flowing with a speed 2 m/s . From this boat, a sound transmitter is lowered into the river through a rigid support. The wavelength of the sound emitted from the transmitter inside the water is 14.45 mm. Assume that attenuation of sound in w... | |
102 | [{"role": "user", "question": "A 500.0 g bird is flying horizontally at 2.25 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar as shown in figure. The bar is uniform, 0.750 m long, has a mass of 1.50 kg, and is hinged at its base. What is the angular velocity of the bar just as it re... | |
1020 | [{"role": "user", "question": "A 300 Hz source, an observer and a wind are moving as shown in the figure with respect to the ground. What frequency is heard by the observer?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7 Hz B: 0.8 Hz C: 10 Hz D: 274 Hz", ... | |
1021 | [{"role": "user", "question": "A wire of length 40 cm which has a mass of 4 g oscillates in its second harmonic and sets the air column in the tube to vibrations in its fundamental mode as shown in figure. Assuming the speedofsoundinairas 340 m/ s,find the tension in the wire.Please directly answer the question and pr... | |
1022 | [{"role": "user", "question": "A source of sound emitting waves at 360 Hz is placed in front of a vertical wall. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Take speed of so... | |
1023 | [{"role": "user", "question": "S_1 and S_2 are two coherent sources of sound having no initial phase difference. The velocity of sound is 330 m/s. No maxima will be formed on the line passing through S_2 and perpendicular to the line joining S_1 and S_2. What is the frequency of both the sources.Please directly answer ... | |
1024 | [{"role": "user", "question": "The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren. (velocityofsoundinair= 330 m/s) Calculate the speed of the motorcyclist,if he does not observe any beats.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, ... | |
1025 | [{"role": "user", "question": "A detector is released from rest over a source of sound of frequency f_0 = 1000 Hz. The frequency observed by the detector at time t is plotted in the graph. Determine the speed of sound in air. Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C,... | |
1026 | [{"role": "user", "question": "Two sources of sound S_1 and S_2 vibrate at the same frequency and are in phase. The intensity of sounddetectedatapoint P is I_0. How many times of I_0 will be intensity of sound detected at P if \\theta = 60\\circ and both the sources are on?Please directly answer the question and provid... | |
1027 | [{"role": "user", "question": "For the wave shown find its frequency and wavelength if its speed is 24 m/s. If the linear density of the string is 0.25 g/m, how much energy is sent down the string per second?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7 ... | |
1028 | [{"role": "user", "question": "A whistle of frequency 540 Hz rotates in a circle of radius 2 m at an angular speed of 15.0 rad/s. What are the maximum frequency heard by a listener, standing at a long distance away at rest from the centre of the circle (sound velocity= 330 m/s).Please directly answer the question and ... | |
1029 | [{"role": "user", "question": "In the Kundt’s tube experiment, the length of the steel rod which is stroked is 120 cm long and the distance between heaps of cork dust is 8 cm when the rod is caused to vibrate longitudinally in air. If the ends of the tube are sealed and the air replaced by a gas and the experiment repe... | |
103 | [{"role": "user", "question": "The magnitudes of the vectors are \\( A = 4.00 \\) and \\( B = 5.00 \\). Find the scalar product \\( \\vec{A} \\cdot \\vec{B} \\) of the two vectors in figure.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2.40 B: 4.50 C: 8.30 ... | |
1030 | [{"role": "user", "question": "When a plane travels with a speed twice the speed of the sound. Calculate the angle of Mach cone.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7 \\circ B: 0.8 \\circ C: 10 \\circ D: 30 \\circ", "answer": "D", "hint": "", "op... | |
1031 | [{"role": "user", "question": "A mass M is hung from two springs suspended from a rigid support as shown. Find the time period, if the extensions of the springs are equal.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0... | |
1032 | [{"role": "user", "question": "As shown in the figure. Find the time period.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi \\sqrt{\\frac{m}{k_1 + k_2}} D: 2\\pi \\sqrt{\\f... | |
1033 | [{"role": "user", "question": "As shown in the figure. Find the time period.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi \\sqrt{\\frac{m}{k_1 + k_2}} D: 2\\pi \\sqrt{\\f... | |
1034 | [{"role": "user", "question": "Two waves traveling in the positive x-direction having same amplitude, same frequency, same speed and phase difference of \\pi/2 between them superimpose. Find the phase of the resultant wave.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D... | |
1035 | [{"role": "user", "question": "Two masses m_1 = 1 kg and m_2 = 0.5 kg are suspended together by a massless spring of spring constant k as shown in figure. When the masses are in equilibrium m_1 is removed without disturbing the system. Calculate the amplitude of oscillations.Please directly answer the question and pro... | |
1036 | [{"role": "user", "question": "A massless spring of spring constant 600 N m^{-1} is used to suspend a body of mass 1 kg. Another body of mass 0.5 kg moving vertically upwards with velocity 3 m s^{-1} hits the suspended body and gets embedded in it. Find the frequency and amplitude of oscillation.Please directly answer... | |
1037 | [{"role": "user", "question": "As shown in the figure. Find the frequency of vibrations of the system for small amplitudes.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi \\... | |
1038 | [{"role": "user", "question": "A whistle emitting a sound of frequency 240 Hz is tied to a string and rotated in the horizontal plane. Determine the highest frequency heard by an observer stationed at a large distance from the whistle. Speed of sound = 320 m/s.Please directly answer the question and provide the correc... | |
1039 | [{"role": "user", "question": "Two pulleys with centers are rotating with the same angular velocity as shown. A bar is placed on top of them, slightly off center. The coefficient of friction between bar and pulleys is m. Find the time period.Please directly answer the question and provide the correct OPTION LETTER ONLY... | |
104 | [{"role": "user", "question": "Vector \\( \\vec{A} \\) has magnitude 6 units and is in the direction of the \\( +x \\)-axis. Vector \\( \\vec{B} \\) has magnitude 4 units and lies in the xy-plane. Find the vector product \\( \\vec{C} = \\vec{A} \\times \\vec{B} \\).Please directly answer the question and provide the co... | |
1040 | [{"role": "user", "question": "Neglect the mass of pulleys and friction. Determine the natural angular frequency of the system.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi... | |
1041 | [{"role": "user", "question": "A uniform solid cylinder of mass m and radius r is released at the position shown (q_0 is small) and it rolls without slipping on the circular track (Radius R) Determine the time periodPlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION... | |
1042 | [{"role": "user", "question": "As shown in the figure Determine the period of small oscillations of the assembly when \\alpha = 0Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7\\pi \\sqrt{\\frac{m}{k_1 + k_2}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\... | |
1043 | [{"role": "user", "question": "A metal rod is clamped as shown. The density and Young’s modulus of the rod are 7000 kg m^{-3} and 1.75 × \\times 10^{11}N/m^2 respectively. Calculate the frequency of natural longitudinal oscillations of the rod.Please directly answer the question and provide the correct OPTION LETTER ON... | |
1044 | [{"role": "user", "question": "Two wires of materials A and B are joined end to end and fixed at both ends with tension all along the wires at 1024 N. The lengths, areas of cross section and densities of the wires A and B are 0.6 m, 0.5 m, 10^{-5} m2, 2 \\times 10^{-5} m2, 4000 kg m^{-3}, 8000 kg m^{-3} respectively. D... | |
1045 | [{"role": "user", "question": "A rigid body of arbitrary shape suspended from a point O, will execute SHM when displaced by a small angle q and released. Now consider the assembly of 3 rods each of mass m and length \\ell, joined at one end as shown. (q = 45\\circ) The distance of the centre of mass of the assembly fro... | |
1046 | [{"role": "user", "question": "A block of mass M attached to a spring of force constant k is in simple harmonic motion having amplitude A_1 and energy E_1. At the instant when the block passes through the equilibrium position, a lump of putty with mass m is placed on the block and the putty sticks. Find the time period... | |
1047 | [{"role": "user", "question": "Two light springs of force constants 3.6 N/m and 6.4 N/m as well as a block of mass 0.4 kg are in one line AB. The distance PQ between the free ends of the spring is 1.2 m. If the block moves along AB with a velocity of 0.9 m/s in between the springs, the time period of oscillation of th... | |
1048 | [{"role": "user", "question": "The mass M attached to the spring does SHM of period \\frac{4\\pi}{10\\sqrt{10}} s. If the 1 kg mass is not to lift off the floor, the amplitude of SHM should be less than?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.14 m ... | |
1049 | [{"role": "user", "question": "Two blocks A and B of masses 0.3 kg and 0.4 kg are stuck to each other one below the other as in the figure by a glue. The spring with force constant equal to 200 N/m. The block B suddenly detach itself from A and falls down free. Then, the total energy of the subsequent oscillation is?P... | |
105 | [{"role": "user", "question": "A motorcyclist heading east through a small town accelerates after he leaves the city limits as shown in figure. Where is he when his speed is \\( 25 \\, \\text{m/s} \\)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 27m B: 55m... | |
1050 | [{"role": "user", "question": "A spring mass system has time period T. Now the spring and the mass are cut into two. Now the period of one spring and one mass is T_1. The period of the other spring and mass is T_2. If the spring and masses are connected as shown the new time period is?Please directly answer the questi... | |
1051 | [{"role": "user", "question": "As shown in the figure The period of oscillation of the system is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 6\\pi \\sqrt{\\frac{M}{5k}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi \\sqrt{\\frac{m}{k_1 + k_2}} D: ... | |
1052 | [{"role": "user", "question": "As shown in the figure The spring constant such that one single spring connected at the centre produces an equivalent effect on the two springs is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \\frac{20k}{9} B: 0.8\\pi \\sqr... | |
1053 | [{"role": "user", "question": "Stiffness of the spring is 147 N/m and block performs simple harmonic motion with amplitude 3 cm. When the block is at the left extreme position, another block, moving directly towards the 1 kg mass with a velocity of 40 cm/s, collides and gets attached to the smaller block. Calculate ang... | |
1054 | [{"role": "user", "question": "A body of mass m = 100 g falls from a height 50 cm on the pan of mass M = 1 kg of a spring balance having a configuration as shown in figure. The force constant of the spring is 110 N/m. The compound body consisting of m and M start vibrating. Find the amplitude of the oscillationsPlease ... | |
1055 | [{"role": "user", "question": "A solid cylinder of mass M = 1 kg is attached to a horizontal massless spring, such that it can roll without slipping. The force constant of the spring is 4 N/m. If the system is released from rest at a position in which the spring is stretched by 0.30 m What is the period and frequency o... | |
1056 | [{"role": "user", "question": "As shown in the figure If the lift suddenly starts moving up with acceleration 2 m/s^2, the amplitude of the resultant SHM is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2 cm B: 0.8 cm C: 10 cm D: 6250 cm", "answer": "A", ... | |
1057 | [{"role": "user", "question": "A block m of mass 1 kg is connected to the back of a truck by a spring of constant 100 N/m. It rests on the smooth surface. If the truck suddenly starts moving with speed 1 m/s, the maximum acceleration of the block is (m/s^2)Please directly answer the question and provide the correct OP... | |
1058 | [{"role": "user", "question": "Two masses of 1 kg each are placed inside a frictionless tube as shown. They are connected by identical springs each of constant 10 N/m. The time period of small oscillations of the system is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D... | |
1059 | [{"role": "user", "question": "A disc can rotate about the axis XX’ The time period of oscillation of the disc is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \\pi \\sqrt{\\frac{m}{k}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2}} C: 10\\pi \\sqrt{\\frac{m}{k_... | |
106 | [{"role": "user", "question": "A motorist traveling at a constant speed passes a school crossing where the speed limit is \\( 10 \\, \\text{m/s} \\) (\\( 36 \\, \\text{km/h} \\), or about \\( 22 \\, \\text{mi/h} \\)). Just as the motorist passes the school-crossing sign, a police officer on a motorcycle stopped there s... | |
1060 | [{"role": "user", "question": "A body of mass m is in the shape of L and is hung as shown. The time period of small oscillations is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2\\pi \\sqrt{\\frac{\\sqrt{10}*a}{3*g}} B: 0.8\\pi \\sqrt{\\frac{m}{k_1 + k_2... | |
1061 | [{"role": "user", "question": "A rope of mass density m is hung as shown. A pulse starts from the point of suspension and travels as shown. If the time taken by the pulse to travel from one end of the rope to the other is T, the time the pulse of the same orientation passes A again is?Please directly answer the questi... | |
1062 | [{"role": "user", "question": "The wave shown is on a string along the x axis, and has equation y = 10\\sin(5x - 3t) m. How many points are moving toward the +y-axis direction?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2 B: 1 C: 3 D: 4 ", "answer": ... | |
1063 | [{"role": "user", "question": "A wire is in the form as shown in figure and is under tension. One part (A) has twice the radius of the other. The ratio of the energies of the incident (from A) and transmitted waves in (B) is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C... | |
1064 | [{"role": "user", "question": "A closed tube with a small opening at one end has fundamental frequency f. If it is dipped vertically in water so that half its length is immersed, the new fundamental frequency is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A... | |
1065 | [{"role": "user", "question": "A car carrying a siren of frequency 1024 Hz is moving with speed 108 kmph towards a wall moving towards it at 36 kmph. The highest frequency heard by the person shown is (v = 330 m/s) approximately?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B... | |
1066 | [{"role": "user", "question": "A body A (m = 1 kg) is attached to the top of a vertically fixed spring of spring constant 1000 N/m and then the mass is released at the initial position P with the spring being initially in its natural length \\ell_0. When A comes back to original position P another body B of equal mass ... | |
1067 | [{"role": "user", "question": "P is held aligned at origin as shown and Q is displaced along x-axis by x and both P and Q are released. The floor on which they are kept is smooth. P reaches maximum speed of 2 m/s when it is 0.2/3 m from origin during the subsequent SHM of the two bodies. Then, what is the value of x?P... | |
1068 | [{"role": "user", "question": "P is held aligned at origin as shown and Q is displaced along x-axis by x and both P and Q are released. The floor on which they are kept is smooth. P reaches maximum speed of 2 m/s when it is 0.2/3 m from origin during the subsequent SHM of the two bodies. Then, what is the value of x?P... | |
1069 | [{"role": "user", "question": "Helium in an open pipe at T_1 = 21\\circ\\text{C} has fundamental f_0 equal to the fundamental of a closed pipe of same length filled with hydrogen at T_2 \\circ\\text{C}. Now both pipes are filled with oxygen at T_2 \\circ\\text{C}. What is T_2?Please directly answer the question and pro... | |
107 | [{"role": "user", "question": "A one-euro coin is dropped from the Leaning Tower of Pisa and falls freely from rest. What are its position after \\( 3.0 \\, \\text{s} \\)? Ignore air resistance.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -35m B: -44m C: -... | |
1070 | [{"role": "user", "question": "A wave travelling on a thin wire represented by Y_1 = 0.01\\sin{200t - 0.1x} (units in metre and second) gets reflected at the junction where the thin wire is joined to a thick wire. The intensity of the reflected wave is 81% of the intensity of the incident wave What is the velocity of t... | |
1071 | [{"role": "user", "question": "A source of frequency f = 144 Hz is rotating about center O, in circle. At a distance OQ = 2R = \\pi m another source of same frequency (144 Hz) is kept and the listener at Q listens to both the sounds What is the minimum period possible between maximum beats and zero beats?Please directl... | |
1072 | [{"role": "user", "question": "A wave source \\( p \\), located at \\( x = 0.25\\,\text{m} \\), begins to oscillate at time \\( t = 0 \\), generating a harmonic transverse wave that propagates along both the positive and negative directions of the \\( x \\)-axis. The wave source stops vibrating at \\( t = 2.0\\,\text{s... | |
1073 | [{"role": "user", "question": "As shown in the figure, two identical wave sources \\( S_1 \\) and \\( S_2 \\) are located at \\( x = -2\\,\\mathrm{m} \\) and \\( x = 12\\,\\mathrm{m} \\) on the x-axis. Both have a vibration period of 4\\,s and an amplitude of 1\\,cm. At \\( t = 0 \\), they start vibrating vertically do... | |
1074 | [{"role": "user", "question": "The block performs simple harmonic motion along the vertical direction. Taking vertically upward as the positive direction, the expression for the block's motion is \\( y = 0.1 \\sin(2.5\\pi t)\\,\\mathrm{m} \\). At \\( t = 0 \\), a small ball is released from rest at a height \\( h \\) a... | |
1075 | [{"role": "user", "question": "A sinusoidal transverse wave propagates to the right. The equilibrium positions of particles \\( P \\) and \\( Q \\) are 0.15\\,m apart. When \\( P \\) reaches its maximum upward displacement, \\( Q \\) is exactly at its maximum downward displacement. What is the most possible wavelength?... | |
1076 | [{"role": "user", "question": "Two sinusoidal transverse waves \\( P \\) and \\( Q \\), both with the same frequency and amplitude \\( A \\), propagate in opposite directions along the \\( +x \\) and \\( -x \\) axes, respectively, within the same medium. The vibration directions of both waves are along the \\( y \\)-ax... | |
1077 | [{"role": "user", "question": "A sinusoidal transverse wave propagates along the positive direction of the \\( x \\)-axis. The solid line represents the wave profile at \\( t = 0 \\), and the dashed line represents the wave profile at \\( t = 0.5\\,\\mathrm{s} \\). It is known that the period of the wave is greater tha... | |
1078 | [{"role": "user", "question": "In a uniform medium, a wave source located at the coordinate origin \\( O \\) performs simple harmonic motion described by \\( y = 5 \\sin\\left(\\frac{\\pi}{2} t\\right) \\). It generates a sinusoidal transverse wave that propagates in the positive direction of the \\( x \\)-axis. At a c... | |
1079 | [{"role": "user", "question": "A sinusoidal transverse wave with a period of \\( 2.0\\,\\mathrm{s} \\) propagates along the \\( x \\)-axis. At a certain moment, the wave profile is as shown in the figure, and at this moment, particle \\( P \\) is moving in the negative direction of the \\( y \\)-axis. What is the speed... | |
108 | [{"role": "user", "question": "a projectile launched as shown in figure. For a given \\( v_0 \\), what value gives maximum horizontal range?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \\( 30^{\\circ} \\) B: \\( 45^{\\circ} \\) C: \\( 60^{\\circ} \\) D: \\... | |
1080 | [{"role": "user", "question": "Figure A shows the waveform of a sinusoidal transverse wave at a certain moment. The horizontal coordinates of particles \\( a \\) and \\( b \\) are \\( x_a = 2\\,\\mathrm{m} \\) and \\( x_b = 6\\,\\mathrm{m} \\), respectively. Figure B shows the vibration graph of particle \\( b \\), sta... | |
1081 | [{"role": "user", "question": "A sinusoidal transverse wave propagates in the positive direction of the \\( x \\)-axis. The wave profile at \\( t = 0 \\) is shown in the figure. The \\( x \\)-coordinate of particle \\( P \\) is \\( 3\\,\\mathrm{m} \\). It is known that the time interval for any vibrating particle to pa... | |
1082 | [{"role": "user", "question": "A sinusoidal transverse wave propagates along a straight line. Taking the moment when the wave source \\( O \\) starts vibrating from its equilibrium position as the zero point of time, the vibration graph of particle \\( A \\) is shown in the figure. It is known that the equilibrium posi... | |
1083 | [{"role": "user", "question": "As shown in the figure, \\( a \\), \\( b \\), \\( c \\), and \\( d \\) are four particles on the \\( x \\)-axis in a uniform medium. The distances between adjacent particles are \\( 2\\,\\mathrm{m} \\), \\( 4\\,\\mathrm{m} \\), and \\( 6\\,\\mathrm{m} \\), respectively. A sinusoidal trans... | |
1084 | [{"role": "user", "question": "The wave profiles at \\( t = 0 \\) and \\( t = 0.20\\,\\mathrm{s} \\) are shown as the solid line and dashed line in the figure, respectively. It is known that the period of the wave satisfies \\( T > 0.20\\,\\mathrm{s} \\). What is the wavelength?Please directly answer the question and p... | |
1085 | [{"role": "user", "question": "Left Figure shows the waveform of a sinusoidal transverse wave at \\( t = 2\\,\\mathrm{s} \\), and Right Figure shows the vibration graph of a particle whose equilibrium position is at \\( x = 1.5\\,\\mathrm{m} \\) in the medium. Particle \\( P \\) is located at the equilibrium position \... | |
1086 | [{"role": "user", "question": "Left Figure shows the waveform of a sinusoidal transverse wave at \\( t = 0.10\\,\\mathrm{s} \\). Particle \\( P \\) is located at the equilibrium position \\( x = 1.0\\,\\mathrm{m} \\), and particle \\( Q \\) is located at \\( x = 4.0\\,\\mathrm{m} \\). Right Figure shows the vibration g... | |
1087 | [{"role": "user", "question": "Left Figure shows the waveform at \\( t = 0 \\), and Figure 2 shows the vibration graph of a certain particle in the medium. Then, a reasonable value for the \\( x \\)-coordinate of this particle is?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B... |
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