instruction stringlengths 53 4.17k | response stringlengths 1 3.48k |
|---|---|
A doughnut-shaped solenoid winding has dimensions $R=1$ meter, diameter of the loop $=10 \mathrm{~cm}$, and the number of windings $=1000$. If a current of $10$ amperes runs through the wire, what is the magnitude of the force on one loop? | The constitutive equation for electric fields in a dielectric medium moving with velocity $v$ in a magnetic field $B$ is
$$
\mathbf{D}=k \varepsilon_{0} \mathbf{E}+\varepsilon_{0}(k-1) \mathbf{v} \times \mathbf{B},
$$
where $k$ is its relative dielectric constant. For a point distance $r$ from the axis of rotation, $... |
In a measurement of $e / m$ for electron using a Thomson type apparatus, i.e., crossed electric and magnetic fields in a cathode-ray tube, it is noted that if the accelerating potential difference is sufficiently large, the ratio $\mathrm{e} / \mathrm{m}$ becomes one-half as large as the accepted value. Take $e / m_{0}... | A Thomson type apparatus is shown schematically in Fig. 2.79, where $V_{1}$ is the accelerating voltage and $V_{2}$ is the deflecting voltage.
Fig. $2.79$ With the addition of a magnetic field $B$ as shown, the electromagnetic field has the action of a velocity-filter. With given values of $V_{1}$ and $V_{2}$, we adju... |
In high energy proton-proton collisions, one or both protons may "diffractively dissociate" into a system of a proton and several charged pions. The reactions are
(1) $p+p \rightarrow p+(p+n \pi)$,
(2) $p+p \rightarrow(p+n \pi)+(p+m \pi)$.
Here $n$ and $m$ count the number of produced pions.
In the laboratory frame... | The energy for the reaction
$$
p+p \rightarrow p+(p+4 \pi)
$$
is minimum when all the final particles are at rest in an inertial frame, particularly the center of mass frame $\Sigma^{\prime}$. Then in the laboratory frame $\Sigma$,
$$
E^{2}-p^{2}=\left(E_{0}+m_{p}\right)^{2}-\left(E_{0}^{2}-m_{p}^{2}\right)=2 m_{p} ... |
Consider a spinless particle represented by the wave function
$$
\psi=K(x+y+2 z) e^{-\alpha r}
$$
where $r=\sqrt{x^{2}+y^{2}+z^{2}}$, and $K$ and $\alpha$ are real constants.
What is the total angular momentum of the particle?
You may find the following expressions for the first few spherical harmonics useful:
$$
... | The wave function may be rewritten in spherical coordinates as
$$
\psi=K r(\cos \phi \sin \theta+\sin \phi \sin \theta+2 \cos \theta) e^{-\alpha r}
$$
its angular part being
$$
\psi(\theta, \phi)=K^{\prime}(\cos \phi \sin \theta+\sin \phi \sin \theta+2 \cos \theta),
$$
where $K^{\prime}$ is the normalization consta... |
In high energy proton-proton collisions, one or both protons may "diffractively dissociate" into a system of a proton and several charged pions. The reactions are
(1) $p+p \rightarrow p+(p+n \pi)$,
(2) $p+p \rightarrow(p+n \pi)+(p+m \pi)$.
Here $n$ and $m$ count the number of produced pions.
In the laboratory frame... | The quantity $E^{2}-p^{2}$ for a system, where we have taken $c=1$ for convenience, is invariant under Lorentz transformation. If the system undergoes a nuclear reaction that conserves energy and momentum, the quantity will also remain the same after the reaction. In particular for a particle of rest mass $m$,
$$
E^{2... |
A Fresnel sone plate is made by dividing a photographic image into 5 separate sones.
The first sone consists of an opaque circular disc of radius $r_{1}$. The second is a concentric transparent ring from $r_{1}$ to $r_{2}$ followed by an opaque ring from $r_{2}$ to $r_{3}$, a second transparent ring from $r_{3}$ to $r... | The focal lengths of the sones are given by
$$
f=\frac{r_{j}^{2}}{j \lambda} .
$$
For $j=1, f=1 \mathrm{~m}, \lambda=5000 \AA$, we have $r_{1}=0.707 \mathrm{~mm}$. |
What is the drift velocity of electrons in a $1 \mathrm{~mm} \mathrm{Cu}$ wire carrying $10 \mathrm{~A}$? | It is $10^{-2} \mathrm{~cm} / \mathrm{sec}$. |
The ground state of the realistic helium atom is of course nondegenerate. However, consider a hypothetical helium atom in which the two electrons are replaced by two identical, spin-one particles of negative charge. Neglect spin-dependent forces. For this hypothetical atom, what is the degeneracy of the ground state? | The two new particles are Bosons; thus the wave function must be symmetrical. In the ground state, the two particles must stay in 1s orbit. Then the space wave function is symmetrical, and consequently the spin wave function is symmetrical too. As $s_{1}=1$ and $s_{2}=1$, the total $S$ has three possible values:
$S=2$... |
Consider the pion photoproduction reaction
$$
\gamma+p \rightarrow p+\pi^{\circ}
$$
where the rest energy is $938 \mathrm{MeV}$ for the proton and $135 \mathrm{MeV}$ for the neutral pion.
If the initial proton is at rest in the laboratory, find the laboratory threshold gamma-ray energy for this reaction to "go". | The quantity $E^{2}-P^{2} c^{2}$ is invariant under Lorentz transformation and for an isolated system is the same before and after a reaction. The threshold $\gamma$-ray energy is that for which the final state particles are all at rest in the center of mass frame. Thus
$$
\left(E_{\gamma}+m_{p} c^{2}\right)^{2}-\left... |
A monochromatic transverse wave with frequency $\nu$ propagates in a direction which makes an angle of $60^{\circ}$ with the $x$-axis in the reference frame $K$ of its source. The source moves in the $x$-direction at speed $v=\frac{4}{5} c$ towards an observer at rest in the $K^{\prime}$ frame (where his $x^{\prime}$-a... | The frame $K$ of the light source moves with velocity $\beta$ c relative to $K^{\prime}$, the observer's frame. The (inverse) transformation of the components of the wave 4 -vector is given by
$$
k_{x}^{\prime} \mathrm{c}=\gamma\left(k_{x} \mathrm{c}+\beta \omega\right), \quad k_{y}^{\prime} \mathrm{c}=k_{y} \mathrm{c... |
Suppose that the ionosphere is in thermal equilibrium at temperature $T$. It consists of electrons (mass $m$ ) and singly charged ions (mass $M$ ). If there were no large-scale electric field, the electrons and ions would have very different scale heights, $k T / m g$ and $k T / M g$ respectively. This would produce a ... | Use a coordinate system with origin at the Earth's surface and the $z$-axis vertically upward. The self-consistent electric field $\mathbf{E}$ is along the $z$ direction:
$$
E=-\frac{\partial V}{\partial z},
$$
or
$$
V=-E z
$$
assuming $E$ to be uniform. Then an electron and an ion at height $z$ will respectively h... |
An electron (mass $m$, charge $e$ ) moves in a plane perpendicular to a uniform magnetic field. If energy loss by radiation is neglected the orbit is a circle of some radius $R$. Let $E$ be the total electron energy, allowing for relativistic kinematics so that $E \gg m c^{2}$.
Compute the needed field induction $B$ n... | In uniform magnetic field $B$ the motion of an electron is described in Gaussian units by
$$
\frac{d p}{d t}=\frac{e}{c} \mathbf{v} \times \mathbf{B},
$$
where $p$ is the momentum of the electron,
$$
\mathbf{p}=m \boldsymbol{v},
$$
with $\gamma=\left(1-\beta^{2}\right)^{-\frac{1}{2}}, \beta=\frac{v}{c}$. Since $\fr... |
Two particles with the same mass $m$ are emitted in the same direction, with momenta $5 m c$ and $10 m c$ respectively. As seen from the slower one, what is the velocity of the faster particle? ($c=$ speed of light.) | In the laboratory frame $K_{0}$, the slower particle has momentum
$$
m \gamma_{1} v_{1}=m \gamma_{1} \beta_{1} c=5 m c
$$
giving
$$
\gamma_{1} \beta_{1}=\sqrt{\gamma_{1}^{2}-1}=5
$$
or
$$
\gamma_{1}^{2}=26
$$
Hence
$$
\beta_{1}^{2}=1-\frac{1}{26}=\frac{25}{26}, \quad \text { or } \quad v_{1}=\sqrt{\frac{25}{26}}... |
When a $5000 \mathrm{lb}$ car driven at $60 \mathrm{mph}$ on a level road is suddenly put into neutral gear (i.e. allowed to coast), the velocity decreases in the following manner:
$$
V=\frac{60}{1+\left(\frac{t}{60}\right)} \mathrm{mph},
$$
where $t$ is the time in sec. Find the horsepower required to drive this car... | Let $V_{0}=60 \mathrm{mph}$, then
$$
\frac{t}{60}=\frac{V_{0}}{V}-1 \text {. }
$$
Hence
$$
\frac{d V}{d t}=\frac{-V^{2}}{60 V_{0}},
$$
and the resistance acting on the car is $F=m V^{2} /\left(60 V_{0}\right)$, where $m$ is the mass of the car. The propulsive force must be equal to the resistance $F^{\prime}$ at th... |
One gram each of ice, water, and water vapor are in equilibrium together in a closed container. The pressure is $4.58 \mathrm{~mm}$ of $\mathrm{Hg}$, the temperature is $0.01^{\circ} \mathrm{C}$. Sixty calories of heat are added to the system. The total volume is kept constant. Calculate the masses of water vapor now p... | It is assumed that the original volume of water vapor is $V$, it volume is also $V$ after heating, and the masses of ice, water, and water vapor are respectively $x, y$ and $z$ at the new equilibrium. We have
$$
\begin{gathered}
x+y+z=3, \\
(1-x) L_{\mathrm{sub}}+(1-y) L_{\mathrm{vap}}=Q=60, \\
\frac{1-x}{\rho_{\mathr... |
The entropy of water at atmospheric pressure and $100^{\circ} \mathrm{C}$ is $0.31$ $\mathrm{cal} / \mathrm{g} \cdot \mathrm{deg}$, and the entropy of steam at the same temperature and pressure is $1.76 \mathrm{cal} / \mathrm{g} \cdot \mathrm{deg}$.
What is the heat of vaporization at this temperature? | Heat of vaporization is
$$
L=T \Delta S=540 \mathrm{cal} / \mathrm{g} .
$$ |
For a particle of mass $m$ in a one-dimensional box of length $l$, the eigenfunctions and energies are
$$
\begin{aligned}
\psi_{n}(x) &=\sqrt{\frac{2}{l}} \sin \frac{n \pi x}{l}, \quad 0 \leq x \leq l \\
E_{n} &=\frac{1}{2 m}\left(\frac{n \pi \hbar}{l}\right)^{2}, \quad n=\pm 1, \pm 2, \ldots
\end{aligned}
$$
Suppose... | First consider the process in which the box length is increased from $l$ to $2 l$. As $t \ll \frac{h}{E_{n}}$, it is reasonable to assume that the state of the particle in the box is unable to respond to the change during such a short time. Therefore the wave function of the particle after the change is completed is
$... |
Given a classical model of the tritium atom with a nucleus of charge $+1$ and a single electron in a circular orbit of radius $r_{0}$, suddenly the nucleus emits a negatron and changes to charge $+2$.
(The emitted negatron escapes rapidly and we can forget about it.) The electron in orbit suddenly has a new situation.
... | As the negatron leaves the system rapidly, we can assume that its leaving has no effect on the position and kinetic energy of the orbiting electron.
From the force relation for the electron,
$$
\frac{m v_{0}^{2}}{r_{0}}=\frac{e^{2}}{4 \pi \varepsilon_{0} r_{0}^{2}},
$$
we find its kinetic energy
$$
\frac{m v_{0}^{2... |
An air-spaced coaxial cable has an inner conductor $0.5 \mathrm{~cm}$ in diameter and an outer conductor $1.5 \mathrm{~cm}$ in diameter. When the inner conductor is at a potential of $+8000 \mathrm{~V}$ with respect to the grounded outer conductor, what is the charge per meter on the inner conductor? | Let the linear charge density for the inner conductor be $\lambda$. By symmetry we see that the field intensity at a point distance $r$ from the axis in the cable between the conductors is radial and its magnitude is given by Gauss' theorem as
$$
E=\frac{\lambda}{2 \pi \varepsilon_{0} r} .
$$
Then the potential diffe... |
A small celestial object, held together only by its self-gravitation, can be disrupted by the tidal forces produced by another massive body, if it comes near enough to that body. For an object of diameter $1 \mathrm{~km}$ and density $2 \mathrm{~g} / \mathrm{cm}^{3}$, find the critical distance from the earth (Roche li... | Suppose the earth is fixed in space and the small celestial object orbits around it at a distance $l$ away as shown in Fig. 1.73. Let $M$ be the mass of the earth, $m$ the mass and $\rho$ the density of the small celestial object. Consider a unit mass of the object on the line $O C$ at distance $x$ from $C$. We have fr... |
A self-luminous object of height $h$ is $40 \mathrm{~cm}$ to the left of a converging lens with a focal length of $10 \mathrm{~cm}$. A second converging lens with a focal length of $20 \mathrm{~cm}$ is $30 \mathrm{~cm}$ to the right of the first lens.
Calculate the distance between the final image and the second lens. | From $\frac{1}{f_{1}}=\frac{1}{u_{1}}+\frac{1}{v_{1}}$, where $f_{1}=10 \mathrm{~cm}, u_{1}=40 \mathrm{~cm}$, we obtain $v_{1}=13 \frac{1}{3} \mathrm{~cm}$.
From $\frac{1}{f_{2}}=\frac{1}{u_{2}}+\frac{1}{v_{2}}$, where $f_{2}=20 \mathrm{~cm}, u_{2}=\left(30-\frac{10}{3}\right) \mathrm{cm}$, we obtain $v_{2}=-100 \math... |
At room temperature, $k_{\mathrm{B}} T / e=26 \mathrm{mV}$. A sample of cadmium sulfide displays a mobile carrier density of $10^{16} \mathrm{~cm}^{-3}$ and a mobility coefficient $\mu=10^{2} \mathrm{~cm}^{2} /$ volt sec.
Calculate the electrical conductivity of this sample. | The electrical conductivity is given by $\sigma=n e \mu$. With $n=10^{22} \mathrm{~m}^{-3}$, $e=1.6 \times 10^{-19} \mathrm{C}, \mu=10^{-2} \mathrm{~m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$, we have for the material $\sigma=$ $16 \Omega^{-1} \mathrm{~m}^{-1}$. |
Consider the situation which arises when a negative muon is captured by an aluminum atom (atomic number $Z=13$ ). After the muon gets inside the "electron cloud" it forms a hydrogen-like muonic atom with the aluminum nucleus. The mass of the muon is $105.7 \mathrm{MeV}$.
(Slide rule accuracy; neglect nuclear motion)
... | For spontaneous transitions from the $3 d$ state, the largest probability is for $3 d \rightarrow 2 p$. In nonrelativistic approximation, the photon energy is given by
$$
\begin{aligned}
h \nu &=\frac{m_{\mu} Z^{2} e^{4}}{2 \hbar^{2}}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right) \\
&=\frac{m_{\mu} c^{2} Z^{2}}{2}\left(... |
The $z$-component of the spin of an electron in free space (no electromagnetic fields) is measured and found to be $+\hbar / 2$. What is the probability of this occuring?
| In the $\sigma_{z}$ representation, the spin wave function is $\left(\begin{array}{l}1 \\ 0\end{array}\right)$, the eigenfunctions of $\sigma_{x}$ are $\frac{1}{\sqrt{2}}\left(\begin{array}{l}1 \\ 1\end{array}\right), \frac{1}{\sqrt{2}}\left(\begin{array}{r}1 \\ -1\end{array}\right)$, corresponding to eigenvalues $+1,-... |
While sitting in front of a color TV with a $25 \mathrm{kV}$ picture tube potential, you have an excellent chance of being irradiated with $\mathrm{X}$-rays.
For the resulting continuous distribution, calculate the shortest wavelength (maximum energy) X-ray. | When a high voltage is applied to the picture tube, electrons emitted from the negative electrode will be accelerated by the electric field to strike the screen target. If the energy of the electrons exceeds a certain value, they can knock off inner-shell electrons in the target atoms and make holes in the inner shells... |
Twenty grams of ice at $0^{\circ} \mathrm{C}$ are dropped into a beaker containing 120 grams of water initially at $70^{\circ} \mathrm{C}$. Find the final temperature of the mixture neglecting the heat capacity of the beaker. Heat of fusion of ice is $80$ $\mathrm{cal} / \mathrm{g}$. | We assume the temperature of equilibrium to be $T$ after mixing. Thus
$$
M_{1} L_{\text {fusion }}+M_{1} C_{p, \text { water }} T=M_{2} C_{p, \text { water }}\left(T_{0}-T\right) .
$$
We substitute $M_{1}=20 \mathrm{~g}, M_{2}=120 \mathrm{~g}, T_{0}=70^{\circ} \mathrm{C}, L_{\text {fusion }}=80 \mathrm{cal} / \mathrm... |
Two conductors are embedded in a material of conductivity $10^{-4} \Omega / \mathrm{m}$ and dielectric constant $\varepsilon=80 \varepsilon_{0}$. The resistance between the two conductors is measured to be $10^{5} \Omega$. Calculate the capacitance between the two conductors. | Suppose that the two conductors carry free charges $Q$ and $-Q$. Consider a closed surface enclosing the conductor with the charge $Q$ (but not the other conductor). We have, using Ohm's and Gauss' laws,
$$
I=\oint \mathbf{j} \cdot d \mathbf{S}=\oint \sigma \mathbf{E} \cdot d \mathbf{S}=\sigma \oint \mathbf{E} \cdot d... |
Consider a large number of $N$ localized particles in an external magnetic field $\mathbf{H}$. Each particle has spin $1 / 2$. Find the number of states accessible to the system as a function of $M_{8}$, the $z$-component of the total spin of the system. Determine the value of $M_{\mathrm{s}}$ for which the number of s... | The spin of a particle has two possible orientations $1 / 2$ and $-1 / 2$. Let the number of particles with spin $1 / 2$ whose direction is along $\mathbf{H}$ be $N_{\uparrow}$ and the number of particles with spin $-1 / 2$ whose direction is opposite to $\mathbf{H}$ be $N_{\downarrow}$; then the component of the total... |
Assume a visible photon of $3 \mathrm{eV}$ energy is absorbed in one of the cones (light sensors) in your eye and stimulates an action potential that produces a $0.07$ volt potential on an optic nerve of $10^{-9} \mathrm{~F}$ capacitance.
Calculate the energy of the action potential. | $Q=V C=0.07 \times 10^{-9}=7 \times 10^{-11}$ Coulomb.$E=\frac{Q V}{2}=\frac{1}{2} \times 7 \times 10^{-11} \times 0.07=2.5 \times 10^{-12}$ joule. |
A spherical dust particle falls through a water mist cloud of uniform density such that the rate of accretion onto the droplet is proportional to the volume of the mist cloud swept out by the droplet per unit time. If the droplet starts from rest in the cloud, find the value of the acceleration of the drop for large ti... | Suppose the spherical dust particle initially has mass $M_{0}$ and radius $R_{0}$. Take the initial position of the dust particle as the origin and the $x$-axis along the downward vertical. Let $M(t)$ and $R(t)$ be the mass and radius of the droplet at time $t$ respectively. Then
$$
M(t)=M_{0}+\frac{4}{3} \pi\left(R^{... |
A solenoid is designed to generate a magnetic field over a large volume. Its dimensions are as follows: length $=2$ meters, radius $=0.1$ meter, number of turns $=1000$.
(Edge effects should be neglected.)
Calculate the self-inductance of the solenoid in Henrys. | inside it is
Suppose the solenoid carries a current $I$. The magnetic induction
$$
B=\mu_{0} n I=\mu_{0} N I / l,
$$
and the magnetic flux linkage is
$$
\psi=N B S=N \frac{\mu_{0} N I}{l} \cdot \pi r^{2}=\frac{I \mu_{0} N^{2} \pi r^{2}}{l} .
$$
Hence the self-inductance is
$$
\begin{aligned}
L=\frac{\psi}{I} &=\f... |
Suppose two compact stars, each of one solar mass, are in a circular orbit around each other with a radius of one solar radius. What is the time scale for decay of this orbit? Take
$$
\begin{aligned}
\text { solar mass } &=2 \times 10^{33} \mathrm{gm}, \\
\text { solar radius } &=7 \times 10^{10} \mathrm{~cm}, \\
G &=... | The total mass-energy of an isolated system is conserved, so it is not possible to radiate monopole gravitational radiation. Also as the total momentum of an isolated system is conserved, which means that the second time derivative of the mass dipole moment $\sum m r$ is zero, it is not possible to radiate dipole gravi... |
A beam of neutral atoms passes through a Stern-Gerlach apparatus. Five equally-spaced lines are observed. What is the total angular momentum of the atom? | When unpolarized neutral atoms of total angular momentum $J$ pass through the Stern-Gerlach apparatus, the incident beam will split into $2 J+1$ lines. Thus $2 J+1=5$, giving $J=2$. |
Calculate the ratio of the mean densities of the earth and the sun from the following approximate data:
$\theta=$ angular diameter of the sun seen from the earth $=\frac{1}{2}^{\circ}$.
$l=$ length of $1^{\circ}$ of latitude on the earth's surface $=100 \mathrm{~km}$.
$t=$ one year $=3 \times 10^{7} \mathrm{~s}$.
$... | Let $r$ be the distance between the sun and the earth, $M_{e}$ and $M_{s}$ be the masses and $R_{e}$ and $R_{s}$ be the radii of the earth and the sun respectively, and $G$ be the gravitational constant. We then have
$$
\begin{aligned}
&\frac{G M_{e} M_{s}}{r^{2}}=M_{e} r \omega^{2}, \\
&\frac{2 R_{s}}{r}=\frac{1}{2} ... |
The latent heat of vaporization of water is about $2.44 \times 10^{6} \mathrm{~J} / \mathrm{kg}$ and the vapor density is $0.598 \mathrm{~kg} / \mathrm{m}^{3}$ at $100^{\circ} \mathrm{C}$. Find the rate of change of the boiling temperature with altitude near sea level in ${ }^{\circ} \mathrm{C}$ per $\mathrm{km}$. Assu... | The Boltzmann distribution gives the pressure change with height:
$$
p(z)=p(0) \exp -\frac{m g z}{k T},
$$
where $p(0)$ is the pressure at sea level $z=0, m$ is the molecular weight of air, and $T_{0}=300 \mathrm{~K}$ is the temperature of the atmosphere. The ClausiusClapeyron equation can be written as
$$
\frac{d p... |
A 55 year old man can focus objects clearly from $100 \mathrm{~cm}$ to $300 \mathrm{~cm}$. Representing the eye as a simple lens $2 \mathrm{~cm}$ from the retina, what is the focal length of the lens at the far point (focussed at $300 \mathrm{~cm}$)? | $\frac{1}{f_{\text {far }}}=\frac{1}{u_{\text {far }}}+\frac{1}{v}, \quad u_{\text {far }}=300 \mathrm{~cm}, v=2 \mathrm{~cm}$.
Solving the equation yields $f_{\text {far }}=1.987 \mathrm{~cm}$. |
A defective satellite of mass $950 \mathrm{~kg}$ is being towed by a spaceship in empty space. The two vessels are connected by a uniform $50 \mathrm{~m}$ rope whose mass per unit length is $1 \mathrm{~kg} / \mathrm{m}$. The spaceship is accelerating in a straight line with acceleration $5 \mathrm{~m} / \mathrm{sec}^{2... | $$
\begin{aligned}
F &=\left(m_{\text {rope }}+m_{\text {gatellite }}\right) \cdot a \\
&=(950+50) \times 5=5 \times 10^{3} \mathrm{~N} .
\end{aligned}
$$ |
The index of refraction of air at $300 \mathrm{~K}$ and 1 atmosphere pressure is $1.0003$ in the middle of the visible spectrum. Assuming an isothermal atmosphere at $300 \mathrm{~K}$, calculate by what factor the earth's atmosphere would have to be more dense to cause light to bend around the earth with the earth's cu... | We are given that
$$
n(r)-1=\rho e^{-\frac{r-f}{s} r b},
$$
where $R=6400 \times 10^{3} \mathrm{~m}$ is the earth's radius and $\rho$ is the density coefficient of air. Then
$$
\begin{gathered}
n(r)=1+\rho e^{-\frac{5 \pi}{500}}, \\
\frac{d n(r)}{d r}=n^{\prime}(r)=-\frac{1}{8700} \rho e^{-\frac{5-8}{500}} .
\end{ga... |
A 100-ohm resistor is held at a constant temperature of $300 \mathrm{~K}$. A current of 10 amperes is passed through the resistor for $300 \mathrm{sec}$.
What is the change in the internal energy of the universe? | As the temperature of the resistor is constant, its state does not change. The entropy is a function of state. Hence the change in the entropy of the resistor is zero: $\Delta S_{1}=0$.The heat that flows from the resistor to the external world (a heat source of constant temperature) is
$$
I^{2} R t=3 \times 10^{6} \m... |
An electron is confined in the ground state of a one-dimensional harmonic oscillator such that $\sqrt{\left\langle(x-\langle x\rangle)^{2}\right\rangle}=10^{-10} \mathrm{~m}$. Find the energy (in $\mathrm{eV})$ required to excite it to its first excited state.
[Hint: The virial theorem can help.] | The virial theorem for a one-dimensional harmonic oscillator states that $\langle T\rangle=\langle V\rangle$. Thus $E_{0}=\langle H\rangle=\langle T\rangle+\langle V\rangle=2\langle V\rangle=m_{e} \omega^{2}\left\langle x^{2}\right\rangle$, or, for the ground state,
$$
\frac{\hbar \omega}{2}=m_{e} \omega^{2}\left\lang... |
$6.0 \times 10^{22}$ atoms of helium gas occupy $2.0$ litres at atmospheric pressure. What is the temperature of the gas?
| Using the equation of state for an ideal gas, we get
$$
T=p V / n k=241 \mathrm{~K} .
$$ |
What is the cohesive energy with respect to separated ions for crystalline $\mathrm{NaCl}$ ? Give the approximate value and a derivation using a very simple model. Lattice constant $a=5.6 \AA$. | For a crystal consisting of $N$ ions, each of charge $\pm e$, the cohesive energy is
$$
U(r)=-\frac{N}{2} \sum_{j}^{\prime}\left[\pm \frac{e^{2}}{r_{l j}}-\frac{b}{r_{l j}^{n}}\right]
$$
where $b$ is the Madelung constant and the prime indicates that $j=l$ is excluded from the summation. With $r_{l j}=\alpha_{j} R$ t... |
Sunlight is normally incident on the surface of water with index of refraction $n=1.33$.
If the incident flux is $1 \mathrm{~kW} / \mathrm{m}^{2}$, what is the pressure that sunlight exerts on the surface of the water? | Fresnel's formulae give for normally incidence
$$
\begin{aligned}
&R=\left(\frac{n_{2}-n_{1}}{n_{2}+n_{1}}\right)^{2}=\left(\frac{n-1}{n+1}\right)^{2}=0.02 \\
&T=\frac{4 n_{1} n_{2}}{\left(n_{2}+n_{1}\right)^{2}}=\frac{4 n}{(n+1)^{2}}=0.98 \\
&R+T=1
\end{aligned}
$$
From the point of view of the photon theory, light ... |
A given type of fuel cell produces electrical energy $W$ by the interaction of $\mathrm{O}_{2}$ fed into one electrode and $\mathrm{H}_{2}$ to the other. These gases are fed in at 1 atmosphere pressure and $298 \mathrm{~K}$, and react isothermally and isobarically to form water. Assuming that the reaction occurs revers... | The chemical equation is
$$
\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}=\mathrm{H}_{2} \mathrm{O} \text {. }
$$
In the reversible process at constant temperature and pressure, the decrease of Gibbs function of the system is equal to the difference between the total external work and the work the system does because of ... |
Calculate the ratio of the intensities of the reflected wave and the incident wave for a light wave incident normally on the surface of a deep body of water with index of refraction $n=1.33$. | Fresnel's equations give for light incident normally
$$
R=\frac{I_{\mathrm{r}}}{I_{\mathrm{i}}}=\left(\frac{n_{2}-n_{1}}{n_{2}+n_{1}}\right)^{2}=0.02 .
$$ |
Čerenkov radiation is emitted by a high energy charged particle which moves through a medium with a velocity greater than the velocity of electromagnetic wave propagation in the medium.
A Čerenkov radiation particle detector is made by fitting a long pipe of one atmosphere, $20^{\circ} \mathrm{C}$ hydrogen gas with an... | As shown in Fig. 5.13, the radiation emitted by the charge at $Q^{\prime}$ at time $t^{\prime}$ arrives at $P$ at time $t$ when the charge is at Q. As the radiation propagates at the speed $c / n$ and the particle has speed $v$ where $v>c / n$, we have
$$
\mathrm{Q}^{\prime} \mathrm{P}=\frac{c}{n}\left(t-t^{\prime}\ri... |
At room temperature, $k_{\mathrm{B}} T / e=26 \mathrm{mV}$. A sample of cadmium sulfide displays a mobile carrier density of $10^{16} \mathrm{~cm}^{-3}$ and a mobility coefficient $\mu=10^{2} \mathrm{~cm}^{2} /$ volt sec.
If the charge carriers have an effective mass equal to $0.1$ times the mass of a free electron, w... | The electrical conductivity is given by $\sigma=n e \mu$. With $n=10^{22} \mathrm{~m}^{-3}$, $e=1.6 \times 10^{-19} \mathrm{C}, \mu=10^{-2} \mathrm{~m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$, we have for the material $\sigma=$ $16 \Omega^{-1} \mathrm{~m}^{-1}$.The law of equipartition of energy
$$
\frac{1}{2} m \bar{v... |
For a rock salt $(\mathrm{NaCl})$ crystal placed in front of the tube, calculate the Bragg angle for a first order reflection maximum at $\lambda=0.5 \AA$. $\left(\rho_{\mathrm{NaCl}}=\right.$ $\left.2.165 \mathrm{~g} / \mathrm{cm}^{3}\right)$ | When a high voltage is applied to the picture tube, electrons emitted from the negative electrode will be accelerated by the electric field to strike the screen target. If the energy of the electrons exceeds a certain value, they can knock off inner-shell electrons in the target atoms and make holes in the inner shells... |
A charge $q=2 \mu \mathrm{C}$ is placed at $a=10 \mathrm{~cm}$ from an infinite grounded conducting plane sheet. Find the force on the charge $q$. | The method of images requires that an image charge $-q$ is placed symmetrically with respect to the plane sheet. This means that the total induced charge on the surface of the conductor is $-q$.The force acting on $+q$ is
$$
F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{(2 a)^{2}}=9 \times 10^{9} \times \frac{\left(2... |
Consider an opaque screen with 5 equally spaced narrow slits (spacing $d$) and with monochromatic plane-wave light (wavelength $\lambda$) incident normally. Assume $d / \lambda=10$. Approximately what is the ratio in intensity of the least intense to the most intense peak? | For multiple-slit interference,
$$
I \propto\left(\frac{\sin \frac{N \delta}{2}}{\sin \frac{\delta}{2}}\right)^{2}=\left(\frac{\sin \frac{5 \pi d \sin \theta}{\lambda}}{\sin \frac{\pi d \ln \theta}{\lambda}}\right)^{2}=\left(\frac{\sin (50 \pi \sin \theta)}{\sin (10 \pi \sin \theta)}\right)^{2} .
$$
For $\theta=0$ to... |
What is the smallest possible time necessary to freeze $2 \mathrm{~kg}$ of water at $0^{\circ} \mathrm{C}$ if a 50 watt motor is available and the outside air (hot reservoir) is at $27^{\circ} \mathrm{C}$ ? | When $2 \mathrm{~kg}$ of water at $0^{\circ} \mathrm{C}$ becomes ice, the heat released is
$$
Q_{2}=1.44 \times 2 \times 10^{3} / 18=1.6 \times 10^{2} \mathrm{kcal} .
$$
The highest efficiency of the motor is
$$
\varepsilon=\frac{T_{2}}{T_{1}-T_{2}}=\frac{Q_{2}}{W_{\min }} .
$$
Thus,
$$
W_{\min }=Q_{2} \frac{T_{1}... |
A gas of molecular hydrogen $\mathrm{H}_{2}$, is originally in equilibrium at a temperature of $1,000 \mathrm{~K}$. It is cooled to $20 \mathrm{~K}$ so quickly that the nuclear spin states of the molecules do not change, although the translational and rotational degrees of freedom do readjust through collisions. What i... | Originally the temperature is high and the para- and orthohydrogen molecules are in equilibrium in a ratio of about $1: 3$. When the system is quickly cooled, for a rather long period the nuclear spin states remain the same. The ratio of parahydrogen to orthohydrogen is still $1: 3$. Now the para- and orthohydrogen are... |
Čerenkov radiation is emitted by a high energy charged particle which moves through a medium with a velocity greater than the velocity of electromagnetic wave propagation in the medium.
Hydrogen gas at one atmosphere and at $20^{\circ} \mathrm{C}$ has an index of refraction $n=1+1.35 \times 10^{-4}$. What is the minim... | As shown in Fig. 5.13, the radiation emitted by the charge at $Q^{\prime}$ at time $t^{\prime}$ arrives at $P$ at time $t$ when the charge is at Q. As the radiation propagates at the speed $c / n$ and the particle has speed $v$ where $v>c / n$, we have
$$
\mathrm{Q}^{\prime} \mathrm{P}=\frac{c}{n}\left(t-t^{\prime}\ri... |
A beam of electrons is fired in free space over a distance of $10^{4} \mathrm{~km}$. If the transversal width of the initial packet is $1 \mu \mathrm{m}$, what will be the minimum spread upon arrival if the kinetic energy of the electrons is $13.6 \mathrm{eV}$ ? | The initial wave packet of an electron in the beam has uncertainties $\Delta p_{x}, \Delta x$ in a transverse direction related by the uncertainty relation
$$
\Delta p_{x} \cdot \Delta x \geq \frac{\hbar}{2} .
$$
If it has momentum $p$, the angle of divergence is
$$
\theta=\frac{\Delta p_{x}}{p} \gtrsim \frac{1}{2 \... |
Assume that the earth's magnetic field is caused by a small current loop located at the center of the earth. Given that the field near the pole is $0.8$ gauss, that the radius of the earth is $R=6 \times 10^{6} \mathrm{~m}$, and that $\mu_{0}=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$, use the Biot-Savart law to cal... | Assume that the axis of the current loop, of small radius a, coincides with the axis of rotation of the earth, which is taken to be the $z$-axis as shown in Fig. 2.8. The contribution of a current element $I d I$ to the magnetic induction $B$ at an axial point $z$ is, according to the Biot-Savart law,
$$
d \mathrm{~B}... |
Consider simple models for the earth's atmosphere. Neglect winds, convection, etc, and neglect variation in gravity.
Assume that the atmosphere is isothermal $\left(\right.$ at $\left.0^{\circ} \mathrm{C}\right)$. By using an expression for the distribution of molecules with height, estimate roughly the height below w... | The molecular number density at height $h$ is denoted by $n(h)$. From the condition of mechanical equilibrium $d p=-n m g d h$ and the equation of state $p=n k T$, we find
$$
\frac{1}{p} d p=-\frac{m g}{k T} d h .
$$
Thus $n(h)=n_{0} \exp (-m g h / k T)$. Let $\int_{0}^{H} n(h) d h / \int_{0}^{\infty} n(h) d h=\frac{... |
A parabolic mirror of small relative aperture ($10 \mathrm{~cm}$ dia, $500 \mathrm{~cm}$ focal length) is used to photograph stars. Roughly what is the diameter of the image "blob" for a star on axis for visible light (take $\lambda=5000 \AA$)? | For photographing stars, the dominant limitation of resolution is the Fraunhofer diffraction by the aperture of the telescope. The diameter of the image "blob" (the Airy disk) of a star on axis is
$$
d=\frac{1.22 \lambda f}{D} .
$$
With $D=10 \mathrm{~cm}, f=500 \mathrm{~cm}$ and $\lambda=5000 \AA$ we have
$$
d=0.3 ... |
A defective satellite of mass $950 \mathrm{~kg}$ is being towed by a spaceship in empty space. The two vessels are connected by a uniform $50 \mathrm{~m}$ rope whose mass per unit length is $1 \mathrm{~kg} / \mathrm{m}$. The spaceship is accelerating in a straight line with acceleration $5 \mathrm{~m} / \mathrm{sec}^{2... | $$
\begin{aligned}
F &=\left(m_{\text {rope }}+m_{\text {gatellite }}\right) \cdot a \\
&=(950+50) \times 5=5 \times 10^{3} \mathrm{~N} .
\end{aligned}
$$ |
Suppose an electron is in a state described by the wave function
$$
\psi=\frac{1}{\sqrt{4 \pi}}\left(e^{i \phi} \sin \theta+\cos \theta\right) g(r)
$$
where
$$
\int_{0}^{\infty}|g(r)|^{2} r^{2} d r=1
$$
and $\phi, \theta$ are the azimuth and polar angles respectively.
What is the expectation value of $L_{z}$ ? | As
$$
Y_{10}=\sqrt{\frac{3}{4 \pi}} \cos \theta, Y_{1, \pm 1}=\mp \sqrt{\frac{3}{8 \pi}} \sin \theta e^{\pm i \phi},
$$
the wave function can be written as
$$
\psi=\sqrt{\frac{1}{3}}\left(-\sqrt{2} Y_{11}+Y_{10}\right) g(r)
$$
Hence the possible values of $L_{z}$ are $+\hbar, 0$.
Since
$$
\begin{aligned}
\int|\ps... |
It is perhaps too easy to think of mathematical truths as objective entities existing in the universe, simply waiting to be "discovered" by brilliant minds such as Pythagoras, Newton, and Descartes. Indeed, such a mentality may be cemented in Western minds raised in the Platonic tradition of a world of ideals that exis... | To answer this question, you must assess evidence. Since this is an EXCEPT question, you're looking for the choice that is not present in the passage. The passage does discuss experiments, choice $\mathrm{A}$, in the section about violation of expectation tests. The part about the $\mathrm{PhD}$ in chemistry who suffer... |
"I acknowledge Shakespeare to be the world's greatest dramatic poet, but regret that no parent could place the uncorrected book in the hands of his daughter, and therefore I have prepared the Family Shakespeare."
Thus did Thomas Bowdler, a self-appointed editor trained as a physician, explain his creation of a children... | Although choices B, C, and D appear in the passage, none of them supports the claim that Bowdler's revised Shakespeare was not universally despised. The quote from Swinburne (choice A), however, does-Swinburne praises Bowdler for creating a Shakespeare that can be put in the hands of children. The correct answer is A. |
The Shawnee people of the Ohio and Cumberland Valleys gave the American elk its other name, wapiti. Yet when we think of elk today, we rarely envision them as eastern animals. If we want to see elk in their natural habitat, we travel to Colorado or Montana, where they still roam the mountainous terrain. Elk were, in fa... | "At present," says the passage, "new herds are established in Arkansas, Kentucky, Michigan, and Wisconsin in addition to Pennsylvania." There is talk of moving herds to Tennessee (choiceA) and the Adirondacks (choice C) in the future. Georgia (choice B) is mentioned only as the original southernmost range of eastern el... |
The Shawnee people of the Ohio and Cumberland Valleys gave the American elk its other name, wapiti. Yet when we think of elk today, we rarely envision them as eastern animals. If we want to see elk in their natural habitat, we travel to Colorado or Montana, where they still roam the mountainous terrain. Elk were, in fa... | As the passage states clearly, "All of the eastern subspecies are now extinct." The reintroduced subspecies is the western subspecies, the one found in Yellowstone. It is a different subspecies from the original Pennsylvania elk. The correct answer is B. |
\section{Passage $\mathrm{V}$}
In linguistics, metathesis refers to the reversal of phonemes in a word. This can come about by accident, as in the common mispronunciation "aks" for ask or the common (and correct) pronunciation of iron as "i-orn." It may come about on purpose, as in various language games.
Accidental me... | Although the origin of Pig Latin appears to be unknown, the author refers to its use in the prisoner-of-war camps of World War II and Vietnam. The implication is that it was used to communicate between prisoners in a language their captors could not understand. The correct answer is D. |
\section{Passage $\mathrm{V}$}
In linguistics, metathesis refers to the reversal of phonemes in a word. This can come about by accident, as in the common mispronunciation "aks" for ask or the common (and correct) pronunciation of iron as "i-orn." It may come about on purpose, as in various language games.
Accidental me... | The final paragraph discusses two forms of metathesis that derive from the butchers' trade. One is louchébem (II), and the other is rechtub klat. Since only II is correct, the answer is choice C. The correct answer is C. |
\section{Passage $\mathrm{V}$}
Engineers and computer scientists are intrigued by the potential power of nanocomputing. Nanocomputers will use atoms and molecules to perform their functions instead of the standard integrated circuits now employed. Theorists believe that the amount of information a nanocomputer could ha... | This question asks you to find the main idea. This passage Passage $\mathrm{V}$ explains that theoretically, a massive amount of computational power is available. However, practical considerations make it unlikely that this limit would ever be reached. Thus choice $\mathrm{C}$ is the best answer. Choice $\mathrm{A}$ is... |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | For vocabulary-in-context questions like this one, always locate the word in question because the distracters are likely to be alternate meanings of that word. Here, the passage states, "Rigoberta's father was taken into custody and tortured when the army believed he had assisted in the assassination of a plantation ow... |
\section{
If our knowledge of the world occurs through the weaving of narratives, as postmodernists would have us believe, then we must judge the truth of each narrative by comparing it with what we value and what we already accept as true. Any metanarrative, or overarching "big story," must be rejected because it atte... | You must make this prediction based on what the author has said in the passage. Two examples of courses in American history are given to support the notion that some mininarratives are incompatible, but there is no indication that offering more courses would help (choice A). The author mentions revising the canon (choi... |
It is perhaps too easy to think of mathematical truths as objective entities existing in the universe, simply waiting to be "discovered" by brilliant minds such as Pythagoras, Newton, and Descartes. Indeed, such a mentality may be cemented in Western minds raised in the Platonic tradition of a world of ideals that exis... | This question asks you to apply new evidence. This question is very difficult because you must understand both the nature of the author's argument and the effect of new evidence on it. The passage argues that mathematical thinking is a product of the innate structures of the brain and mathematical "truths" are created ... |
\section{Passage $\mathrm{V}$}
Engineers and computer scientists are intrigued by the potential power of nanocomputing. Nanocomputers will use atoms and molecules to perform their functions instead of the standard integrated circuits now employed. Theorists believe that the amount of information a nanocomputer could ha... | This question asks about supporting details and evidence. Go back to the passage and find why the author believes technology may reach the theoretical limit discussed. In the last paragraph, the author indicates that each technological advance provides the basis for further evolution, as choice B states. Choice A refer... |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | “The Red Cross, yes, but Henry Kissinger?" asks the author. The author finds the controversy over Rigoberta "surprising" and states, "her place in the history of Central American peasant revolutions seems assured." That indicates that as far as the author is concerned, the committee's choice of Rigoberta is not undeser... |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | The question asks you to find the one or more statements that do NOT support the premise that Rigoberta falsified her book. To do that, you must find the statements that do support that premise and eliminate those. Statements that do support the premise will indicate some kind of disconnect between what she said and wh... |
\section{
If our knowledge of the world occurs through the weaving of narratives, as postmodernists would have us believe, then we must judge the truth of each narrative by comparing it with what we value and what we already accept as true. Any metanarrative, or overarching "big story," must be rejected because it atte... | Smorgasbord is a Swedish word meaning "a buffet meal featuring a variety of dishes." It is this variety, or choice, to which the author refers. Even if you do not know the word, you should be able to guess this from context. The correct answer is B. |
\section{
If our knowledge of the world occurs through the weaving of narratives, as postmodernists would have us believe, then we must judge the truth of each narrative by comparing it with what we value and what we already accept as true. Any metanarrative, or overarching "big story," must be rejected because it atte... | Supposition I is supported by the examples of competing American history courses. Supposition II is supported by the clash between evolutionary theory and strict Bible interpretation. Supposition III is supported by the example of a Eurocentric look at American history (see paragraph 2). Since all three suppositions ar... |
\section{
Language consists of three main parts. The first is simply vocabulary, the lexicon of words available to the speaker to describe particular concepts, actions, and states. The second part is morphology, the set of rules that dictates how words and parts of words may be combined to form other words. The final p... | This application question asks you to draw conclusions. The author states that the English language makes do with fewer verb forms than other languages, but it still can convey different meanings. This makes choice A correct. Choices B and D are not supported by the passage, and choice C reflects what some linguists be... |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | You are asked here to assess the relative relevance of evidence. Falsifying a birth date (choice A) might be evidence of a minor deception, but it would not be enough to support charges of fraud. Falsifying a critical part of her history as it relates to her reputation, as choice C would do, would certainly indicate a ... |
\section{
If our knowledge of the world occurs through the weaving of narratives, as postmodernists would have us believe, then we must judge the truth of each narrative by comparing it with what we value and what we already accept as true. Any metanarrative, or overarching "big story," must be rejected because it atte... | All three philosophies are all-encompassing ways to look at the world, so all three could be considered metanarratives. Since all three are valid, the answer is choice $\mathrm{D}$. The correct answer is D. |
It is perhaps too easy to think of mathematical truths as objective entities existing in the universe, simply waiting to be "discovered" by brilliant minds such as Pythagoras, Newton, and Descartes. Indeed, such a mentality may be cemented in Western minds raised in the Platonic tradition of a world of ideals that exis... | In order to answer this question, you must be able to judge credibility. The author cites the violation of expectation experiment as support for the author's claim that mathematics is an innate part of human cognition. In order for these experiments to be credible, the author is assuming that the researchers can accura... |
In sharp contrast to the modern, confessional poetry of the 20th century, the oeuvre of Henry Wadsworth Longfellow seems quaint and primly Victorian. During his lifetime, however, he was the most celebrated poet in the country. A closer look at the history of American poetry reveals that, despite his eminence, Longfell... | This question asks you to assess evidence. To answer it, first note the hypothesis as stated in the question stem: Whitman was responsible for the radical shift in American poetry. Then determine which statements support it and which one does not. The one that does not is the correct answer. The fact that his poetry wa... |
\section{Passage $\mathrm{V}$}
Engineers and computer scientists are intrigued by the potential power of nanocomputing. Nanocomputers will use atoms and molecules to perform their functions instead of the standard integrated circuits now employed. Theorists believe that the amount of information a nanocomputer could ha... | The question asks you to solve a problem. To answer it, you must first understand how computational power is calculated. The passage states that the power is found by dividing the total energy by the energy required for an operation. Decreasing the amount of energy, as in choice $\mathrm{C}$, would yield a larger quoti... |
"I acknowledge Shakespeare to be the world's greatest dramatic poet, but regret that no parent could place the uncorrected book in the hands of his daughter, and therefore I have prepared the Family Shakespeare."
Thus did Thomas Bowdler, a self-appointed editor trained as a physician, explain his creation of a children... | Bowdler himself was trained as a doctor; the passage makes clear that he was not an editor. His sister, however, was a poet and editor, and therefore was more likely than he to have made the editorial changes that led to the revised Shakespearean texts. There is no evidence in the passage to support choice $\mathrm{C}$... |
\section{
Language consists of three main parts. The first is simply vocabulary, the lexicon of words available to the speaker to describe particular concepts, actions, and states. The second part is morphology, the set of rules that dictates how words and parts of words may be combined to form other words. The final p... | This question asks about supporting details. The passage states that the present tense (statement I) is usually expressed using the stem form of the verb, but can also be expressed in the third-person singular by using the $-s$ suffix. Similarly, verbal adjectives (statement II) are sometimes expressed using the -ing s... |
The man whom Franklin Delano Roosevelt christened “The Happy Warrior" in a nominating speech would later become a thorn in Roosevelt's side. Some thought the switch in loyalties was sour grapes, but others saw Alfred E. Smith as the epitome of William Wordsworth's "happy warrior" and therefore a man who "makes his mora... | Smith was a progressive born of immigrant parents, and he supported both civil liberties and unions, as well as "those he saw as most in need of government's assistance." Of the answers given, only choice A is likely. This question requires you to combine information. The correct answer is A. |
\section{
Language consists of three main parts. The first is simply vocabulary, the lexicon of words available to the speaker to describe particular concepts, actions, and states. The second part is morphology, the set of rules that dictates how words and parts of words may be combined to form other words. The final p... | This question involves analyzing an argument. Statement $\mathrm{I}$ is supported by the examples of the Spanish language and the Kivunjo language, which have far more forms than the English language. Statement II is unsupported by a specific example. Statement III is supported by the example in the final paragraph of ... |
"I acknowledge Shakespeare to be the world's greatest dramatic poet, but regret that no parent could place the uncorrected book in the hands of his daughter, and therefore I have prepared the Family Shakespeare."
Thus did Thomas Bowdler, a self-appointed editor trained as a physician, explain his creation of a children... | Look for the answer that is supported by the text. Although choices A, B, and C may in fact be true, none of them receives support in the passage. The author's reason for including mention of Nehum Tate is to show that the Bowdlers were not the first to edit Shakespeare. The correct answer is D. |
The Shawnee people of the Ohio and Cumberland Valleys gave the American elk its other name, wapiti. Yet when we think of elk today, we rarely envision them as eastern animals. If we want to see elk in their natural habitat, we travel to Colorado or Montana, where they still roam the mountainous terrain. Elk were, in fa... | The claim is that elk reintroduction benefits other species. Your answer must contradict this contention. Choice A shows a clear benefit to other populations, so it does not contradict the claim. Choice B shows a change in a species that does not live where elk live. Choice D does not refer to other species at all. Onl... |
\section{Passage $\mathrm{V}$}
In linguistics, metathesis refers to the reversal of phonemes in a word. This can come about by accident, as in the common mispronunciation "aks" for ask or the common (and correct) pronunciation of iron as "i-orn." It may come about on purpose, as in various language games.
Accidental me... | Spooner was known for his transpositions, of which "You have deliberately tasted two worms" (wasted two terms) is an example. Although transposition has a variety of possible meanings, here it refers specifically to the exchange of letters or word parts. The correct answer is A. |
Biologists use the term "living fossil" to designate a species that maintains many of the features of its ancient ancestors. These species have evidenced very little evolutionary change, indicating not that they are primitive creatures as might be popularly believed, but instead that they are exquisitely suited for the... | This question asks you to compare and contrast information found in the passage. We know from the second paragraph that the horseshoe crab is the most recent living fossil at 200 million years old. The other three all date from around 400 million years ago. The final paragraph says that at that time, land-dwelling plan... |
\section{Passage $\mathrm{V}$}
In linguistics, metathesis refers to the reversal of phonemes in a word. This can come about by accident, as in the common mispronunciation "aks" for ask or the common (and correct) pronunciation of iron as "i-orn." It may come about on purpose, as in various language games.
Accidental me... | If most Spoonerisms are apocryphal, or fictional, that would not be proved by a list of attributed transpositions (choice A), which would simply seem to support their authenticity. Examples of modern-day transpositions (choice B) would do nothing to support or deny the authenticity of Spoonerisms, and Spooner's letters... |
The man whom Franklin Delano Roosevelt christened “The Happy Warrior" in a nominating speech would later become a thorn in Roosevelt's side. Some thought the switch in loyalties was sour grapes, but others saw Alfred E. Smith as the epitome of William Wordsworth's "happy warrior" and therefore a man who "makes his mora... | Although choice A may be true, only choice B is alluded to in the passage, allowing you to draw conclusions. New York City, says the author, was "viewed even in the early twentieth century as disconnected from the national character." The correct answer is B. |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | This question is purely speculative, since the author did not include information to support the statement. If the author had, it would have had to be information that told more about the teaching of Rigoberta's book in schools. Two students' comments (choice A) would not be enough evidence, and choices B and C might s... |
It is perhaps too easy to think of mathematical truths as objective entities existing in the universe, simply waiting to be "discovered" by brilliant minds such as Pythagoras, Newton, and Descartes. Indeed, such a mentality may be cemented in Western minds raised in the Platonic tradition of a world of ideals that exis... | This question asks you to draw conclusions about an assertion that is not directly stated. The second paragraph states that mathematics is created by man, which implies that mathematical concepts are to some degree arbitrary. Choice A is contradicted by the passage in the final paragraph when the author says that the a... |
\section{
If our knowledge of the world occurs through the weaving of narratives, as postmodernists would have us believe, then we must judge the truth of each narrative by comparing it with what we value and what we already accept as true. Any metanarrative, or overarching "big story," must be rejected because it atte... | The main idea of the passage has to do with the tension between metanarratives and mininarratives, especially as they affect the way we learn things. This would be most useful for people who develop curricula. The correct answer is B. |
Biologists use the term "living fossil" to designate a species that maintains many of the features of its ancient ancestors. These species have evidenced very little evolutionary change, indicating not that they are primitive creatures as might be popularly believed, but instead that they are exquisitely suited for the... | This question requires you to find the main idea. The passage discusses living fossils, a term biologists use to designate a species that has changed little since its inception. It then provides details on four different living fossils. Choice D is the best description of the passage. The passage doesn't primarily expl... |
The Shawnee people of the Ohio and Cumberland Valleys gave the American elk its other name, wapiti. Yet when we think of elk today, we rarely envision them as eastern animals. If we want to see elk in their natural habitat, we travel to Colorado or Montana, where they still roam the mountainous terrain. Elk were, in fa... | Hunting and habitat destruction are the only reasons mentioned for the depopulation of elk prior to the 20th century. The correct answer is D. |
\section{Passage $\mathrm{V}$}
Engineers and computer scientists are intrigued by the potential power of nanocomputing. Nanocomputers will use atoms and molecules to perform their functions instead of the standard integrated circuits now employed. Theorists believe that the amount of information a nanocomputer could ha... | You are asked to draw a conclusion in order to answer this question. The author indicates that choices $\mathrm{B}$ and $\mathrm{D}$ are still in the realm of the theoretical. The author also states that the memory limit in choice $\mathrm{C}$ may be "exceeded." That leaves choice A, which is supported when the author ... |
\section{Passage $\mathrm{V}$}
The Nobel Peace Prize has often engendered controversy. The Red Cross, yes, but Henry Kissinger? Mother Teresa, perhaps, but Yasser Arafat? Surprisingly, a loud and ongoing controversy surrounds a choice that at first look seems most benign-that of the Guatemalan freedom fighter, Rigobert... | This question calls for a cause-and-effect relationship. You must find the cause of Rigoberta's departure. That is not simply something that happened before her departure (choice D), or something that was true but not a direct cause (choice A). The cause appears in the sentence "Soon Rigoberta was herself a target." Sh... |
\section{Passage $\mathrm{V}$}
In linguistics, metathesis refers to the reversal of phonemes in a word. This can come about by accident, as in the common mispronunciation "aks" for ask or the common (and correct) pronunciation of iron as "i-orn." It may come about on purpose, as in various language games.
Accidental me... | Verlan and other backslang (I) are word games and therefore purposeful, not accidental. The examples of accidental metathesis include the change between Latin originals and Spanish derivatives (II) and mispronunciations or skewed pronunciations of English words (III). Since II and III are correct, the answer is choice ... |
It is perhaps too easy to think of mathematical truths as objective entities existing in the universe, simply waiting to be "discovered" by brilliant minds such as Pythagoras, Newton, and Descartes. Indeed, such a mentality may be cemented in Western minds raised in the Platonic tradition of a world of ideals that exis... | This evaluation question asks you to analyze an argument. Specifically, you need to figure out why the author mentioned the Platonic tradition. In the first paragraph, the author states that the prevailing view of mathematics is an "easy" one that may be "cemented" in the minds of people. Later, in the third paragraph,... |
\section{Passage $\mathrm{V}$}
Engineers and computer scientists are intrigued by the potential power of nanocomputing. Nanocomputers will use atoms and molecules to perform their functions instead of the standard integrated circuits now employed. Theorists believe that the amount of information a nanocomputer could ha... | This question requires you to combine information. The passage discusses computers, technology, and even physics. However, the information is presented at the level of someone with a casual, rather than expert, knowledge of these fields. Thus choice D would be the best answer. Choice A may be close, but the information... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.