112 年 國立中山大學物理學系碩士班《普通物理學》

Which of the following is a correct unit for Newton's gravitational constant?
(A) $\frac{m^3}{kg^2 \cdot s^2}$
(B) $\frac{m^3}{kg \cdot s^2}$
(C) $\frac{m}{kg^2 \cdot s^2}$
(D) $\frac{m}{kg \cdot s^2}$

Which physical quantity in a system is conserved if the only force exerted on the system is a conserved force?
(A) momentum
(B) angular momentum
(C) mechanical energy
(D) energy potential

If a free electron with charge -e and mass m moving at speed v enters a region with a magnetic field and makes a circular motion of radius r, what is the magnitude of the magnetic field?
(A) $\frac{mv}{er}$
(B) $\frac{mv}{er^2}$
(C) $\frac{m^2v}{er}$
(D) $\frac{mv^2}{er}$

It is known that water is considered incompressible. However, the water stream from the faucet is usually narrower at the bottom than at the top. Which of the following mechanisms best explains this phenomenon?
(A) electric force
(B) magnetic force
(C) mass conservation
(D) momentum conservation

An ant of mass m rests on a stationary wheel of radius r with inertia $I = cr^2$ before moving counterclockwise with speed v. If the rotational friction of the wheel is negligible, how much angle does the wheel turn when the ant passes its original spot on the wheel for the first time?
(A) $\frac{2\pi r}{v(c+m)}$
(B) $\frac{2\pi (c-m)}{v}$
(C) $\frac{2\pi mr}{vc}$
(D) $\frac{2\pi r}{v(c+m)}$

Assuming the exit speed of cannonballs is always the same when fired from the cannon, the angle of the cannon is $\varphi$ when aiming at a target $800\ \mathrm{m}$ away. What is the condition on angle $\theta$ when aiming at a target $300\ \mathrm{m}$ away?

(A) $\sin(2\theta)=\frac{3}{8}\sin(2\varphi)$
(B) $\cos(\theta)=\frac{3}{8}\cos(\varphi)$
(C) $\tan(\theta)=\frac{3}{8}\tan(\varphi)$
(D) $\tan(\theta)=\frac{9}{64}\tan(\varphi)$

The heat capacity of object A is three times that of object B, and the initial temperatures of objects A and B are $300\ \mathrm{K}$ and $600\ \mathrm{K}$, respectively. What is the final temperature of both objects if they are in thermal contact and isolated from the environment?

(A) $430\ \mathrm{K}$
(B) $525\ \mathrm{K}$
(C) $400\ \mathrm{K}$
(D) $375\ \mathrm{K}$

Which of the following descriptions about an inelastic collision is true?

(A) Momentum is not conserved, but kinetic energy is conserved.
(B) Total mass is not conserved, but momentum is conserved.
(C) Neither kinetic energy nor momentum is conserved.
(D) Momentum is conserved, but kinetic energy is not conserved.

A stationary source of sound emits a sound wave of frequency $f$. If a flight flies toward the source at the speed of sound, what frequency does the flight observe?

(A) $f/2$
(B) $f$
(C) $2f$
(D) cannot hear the sound

A $40\text{-N}$ uniform plank leans against a frictionless wall, as shown in Fig. 1. What is the torque (about point P) applied to the plank by the wall?

Figure 1. A plank leans on a frictionless wall. 🖼️【此處有附圖，請對照原卷】

(A) $60\ \mathrm{m\cdot N}$
(B) $30\ \mathrm{m\cdot N}$
(C) $120\ \mathrm{m\cdot N}$
(D) $80\ \mathrm{m\cdot N}$

A wooden ball floats in a fluid of density $13.5\ \mathrm{g/mL}$ with $20\%$ of its volume under the fluid. What is the density of the wood?

(A) $5.0\ \mathrm{g/mL}$
(B) $2.7\ \mathrm{g/mL}$
(C) $10.8\ \mathrm{g/mL}$
(D) $3.4\ \mathrm{g/mL}$

Two identical conducting spheres, one carrying charge $Q$ and the other neutral, touch each other and are then separated by distance $r$. What is the magnitude of the electrostatic force between the conducting spheres?

(A) $\frac{Q^2}{2\pi\varepsilon_0r^2}$
(B) $\frac{Q^2}{4\pi\varepsilon_0r^2}$
(C) $\frac{Q^2}{8\pi\varepsilon_0r^2}$
(D) $\frac{Q^2}{16\pi\varepsilon_0r^2}$

What is the total work to move a point charge of charge $q$ from point a to point b shown in Fig. 2? The other two charges in the system both carry charge $Q$.

Figure 2. Moving charge from position a to b. 🖼️【此處有附圖，請對照原卷】

(A) $\frac{qQ}{\pi\varepsilon_0d}$
(B) $\frac{5qQ}{16\pi\varepsilon_0d}$
(C) $0$
(D) $\frac{5qQ}{8\pi\varepsilon_0d}$

A $5.0\ \mathrm{kg}$ package is moving at a speed of $20.0\ \mathrm{m/s}$ vertically upward when it explodes into three fragments: a $1.00\ \mathrm{kg}$ fragment is shot upward with an initial speed of $10.0\ \mathrm{m/s}$, and a $2.00\ \mathrm{kg}$ fragment is shot horizontally with an initial speed of $10.0\ \mathrm{m/s}$. What is the total kinetic energy provided by the explosion?

(A) $8.0\times10^2\ \mathrm{J}$
(B) $5.7\times10^2\ \mathrm{J}$
(C) $2.8\times10^3\ \mathrm{J}$
(D) $1.3\times10^3\ \mathrm{J}$

Two parallel wires, $4.0\ \mathrm{cm}$ apart, both carry currents of $2.0\ \mathrm{A}$ in the same direction. What is the force per unit length of one wire on the other? ($\mu_0=1.3\times10^{-6}\ \mathrm{N\cdot A^{-2}}$)

(A) $2.0\times10^{-5}\ \mathrm{N/m}$, attractive
(B) $1.1\times10^{-5}\ \mathrm{N/m}$, attractive
(C) $2.0\times10^{-5}\ \mathrm{N/m}$, repulsive
(D) $1.1\times10^{-5}\ \mathrm{N/m}$, repulsive

The magnitude of the magnetic field outside of a long ideal solenoid of $n$ turns per unit length with current $I$ is:

(A) $0$
(B) $\mu_0nI$
(C) $\frac{\mu_0n}{I}$
(D) $\frac{\mu_0I}{n}$

A particle with charge $q$ is brought from far away to a point near an electric dipole. No total work is done if the final position of the particle is on:

(A) a line that is perpendicular to the dipole moment.
(B) the line through the charges of the dipole.
(C) a line that makes an angle of $45^\circ$ with the dipole moment.
(D) none of the above.

The effective resistance from a to b in Fig. 3 is $4.0\ \Omega$. What is the resistance of each individual resistor in the circuit? The resistances of all the individual resistors are the same.

Figure 3. A circuit composed of 5 identical resistors effectively works as a $4.0\text{-}\Omega$ resistor. 🖼️【此處有附圖，請對照原卷】

(A) $4.0\ \Omega$
(B) $2.0\ \Omega$
(C) $8.0\ \Omega$
(D) $0.8\ \Omega$

As shown in Fig. 4, an $m_1=1.0\ \mathrm{kg}$ block is placed on top of an $m_2=8.0\ \mathrm{kg}$ block, which lies on a frictionless surface. The coefficient of kinetic friction between the two blocks is $0.20$; they are connected via a pulley and a string. A hanging block of mass $m_3=6.0\ \mathrm{kg}$ is connected to the $m_2$ block via another pulley and string. Both strings are massless and the pulleys are frictionless. What is the acceleration magnitude of the blocks? (Gravitational acceleration $g=9.8\ \mathrm{m/s^2}$)

Figure 4. A system composed of three blocks, strings, and pulleys. 🖼️【此處有附圖，請對照原卷】

(A) $3.7\ \mathrm{m/s^2}$
(B) $2.7\ \mathrm{m/s^2}$
(C) $9.7\ \mathrm{m/s^2}$
(D) $8.0\ \mathrm{m/s^2}$

A uniform plate of mass $M$ is placed on two fast-rotating identical wheels of radius $r$. The coefficients of kinetic friction between the plate and both wheels are $\mu$, the distance between the centers of the two wheels is $\ell$, the wheel on the right (left) rotates counterclockwise (clockwise) with angular speed $\omega$, and the gravitational acceleration is denoted by $g$. If the mass center of the plate is displaced by $d$ from the center of the two wheels, what is the frequency the plate oscillates with? Assume the plate is so heavy that it always stays on the wheels.

Figure 5. A plate of mass $M$ is placed on two rotating wheels making an oscillating motion. 🖼️【此處有附圖，請對照原卷】

(A) $\omega$
(B) $\frac{\omega d}{r}$
(C) $\sqrt{\frac{2\mu gd}{\ell r}}$
(D) $\sqrt{\frac{2\mu g}{\ell}}$