103年 - 103 國立中山大學轉學生招生考試試題_物理系二年級：普通物理#139283

1. Four particles are moving on a plane under the same constant acceleration \( \vec{a} = \hat{y} \), each having its initial velocity vector as follows: (a)\( 10\hat{x}+10\hat{y} \), (b)\( 10\hat{x}+8\hat{y} \), (c)\( 8\hat{x}+10\hat{y} \), (d)\( 12\hat{x}+12\hat{y} \). If the respective displacements are \( R_a \), \( R_b \), \( R_c \), \( R_d \), which of the following is correct?(A)\( R_a ＞ R_b ＞ R_c ＞ R_d \)(B)\( R_c ＞ R_b ＞ R_d ＞ R_a \)(C)\( R_d ＞ R_a ＞ R_b ＞ R_c \)(D)\( R_d ＞ R_a ＞ R_c ＞ R_b \)
(E)\( R_a ＞ R_c ＞ R_b ＞ R_d \)

2. Given a position vector \( \vec{r} = (-t^2+1)\hat{i} + (3t-5)\hat{j} + (t^2-2t+2)\hat{k} \), find the magnitude of acceleration at t=1.(A)\( \sqrt{5} \)(B)\( \sqrt{14} \)(C)\( 2\sqrt{2} \)(D)2
(E)0

3. What is the rotational inertia of a solid sphere about an axis that passes through the spherical center? (Assume the radius is R and mass is M.)(A)\( \frac{1}{2}MR^2 \)(B)\( \frac{2}{3}MR^2 \)(C)\( \frac{1}{4}MR^2 \)(D)\( \frac{2}{5}MR^2 \)
(E)\( MR^2 \)

4. A man of mass m falls from rest at point A that is at a horizontal distance of D from the origin O of an xyz coordinate system, i.e., A = (D, 0, 0). Assuming gravity \( \vec{g} = -g\hat{z} \). What is the angular momentum of the falling man about O at time t?(A)\( Dmgt\hat{x} \)(B)\( \frac{1}{2}Dmgt\hat{x} \)(C)\( Dmgt\hat{y} \)(D)\( \frac{1}{2}Dmgt\hat{y} \)
(E)\( -\frac{1}{2}Dmgt\hat{z} \)

5. Which wheel is at equilibrium?(A)(B)(C)(D)
(E)E

6. If the mass density of the Earth is \( \rho \), for a tunnel drilled through between the north and south poles, what is the period of oscillation of a particle pulled by the gravity and moving without friction in the tunnel from one pole to the other?(A)\( \sqrt{\frac{3\pi}{G\rho}} \)(B)\( \sqrt{\frac{3\pi}{4G\rho}} \)(C)\( \sqrt{\frac{3}{4\pi G\rho}} \)(D)\( \sqrt{\frac{3\pi}{2G\rho}} \)
(E)\( \sqrt{\frac{4\pi}{G\rho}} \)

7. A linear SHM occurs at a frequency of f=2Hz. If initially at t=0 the displacement x(t) is x(0)=3, and the velocity v(0)=0, what is v(0.5)?(A)0(B)\( \pi \)(C)\( 2\pi \)(D)\( 3\pi \)
(E)\( 6\pi \)

8. A sound source of frequency f moves at a velocity of \( v_s \), while a detector moves at \( v_d \) in parallel. If the speed of the sound in air is v, what is the frequency of the sound as measured by the detector?(A)\( \frac{v+v_d}{v+v_s}f \)(B)\( \frac{v-v_d}{v-v_s}f \)(C)\( \frac{v+v_s}{v+v_d}f \)(D)\( \frac{v-v_d}{v+v_s}f \)
(E)\( \frac{v+v_s}{v-v_d}f \)

9. What is the heat capacity of two connected metals, each with masses \( M_1 \) and \( M_2 \) and specific heats of \( X_1 \) and \( X_2 \)?(A)\( \frac{X_1}{M_1} + \frac{X_2}{M_2} \)(B)\( \frac{M_1}{X_1} + \frac{M_2}{X_2} \)(C)\( M_1X_1 + M_2X_2 \)(D)\( \frac{X_1+X_2}{M_1+M_2} \)
(E)\( \frac{M_1+M_2}{X_1+X_2} \)

10. For a particle of temperature T located in an environment \( T_{env} \), what is the temperature dependence of thermal radiation energy that is emitted from the particle?(A)\( T^4 \)(B)\( T^4_{env} \)(C)\( T^4 - T^4_{env} \)(D)\( T \)
(E)\( T_{env} \)

11. The speed of molecules in an ideal gas follows Maxwell's distribution law. Which of the following is correct when comparing the average speed \( v_a \), most probable speed \( v_p \), and root mean square speed \( v_{rms} \)?(A)\( v_p ＞ v_a ＞ v_{rms} \)(B)\( v_{rms} ＞ v_a ＞ v_p \)(C)\( v_{rms} ＞ v_p ＞ v_a \)(D)\( v_a ＞ v_{rms} ＞ v_p \)
(E)\( v_p ＞ v_{rms} ＞ v_a \)

12. A point charge Q is located at a distance of R/2 from the center of a spherical shell of radius R. If the shell is electrically neutral, what is the net flux of electric field through the sphere shell?(A)\( Q \)(B)\( \varepsilon_0 Q \)(C)\( Q/\varepsilon_0 \)(D)0
(E)\( Q/2 \)

13. Three point charges held at the corner of an equilateral triangle whose length of each side is d. If \( Q_1=+q \), \( Q_2=+2q \), \( Q_3=-3q \), the total electrostatic energy is(A)\( \frac{6q^2}{4\pi\varepsilon_0 d} \)(B)\( \frac{-6q^2}{4\pi\varepsilon_0 d} \)(C)\( \frac{7q^2}{4\pi\varepsilon_0 d} \)(D)\( \frac{-7q^2}{4\pi\varepsilon_0 d} \)
(E)0

14. An RC circuit consists of a resistor, a capacitor, and an idea batter of emf \( \varepsilon \) in series. During a charging process, what is the charge in the capacitor after a time t=RC? (Note: e = 2.7183 and 1/e = 0.3679)(A)\( 0.37C\varepsilon \)(B)\( 0.5C\varepsilon \)(C)\( 0.63C\varepsilon \)(D)\( C\varepsilon \)
(E)0

15. A long straight wire of radius R carries a uniformly distributed current i. What is the magnetic field at a distance r<R from the center of the wire?(A)0(B)\( \frac{\mu_0 i}{2\pi r} \)(C)\( \frac{\mu_0 i}{2\pi R} \)(D)\( \frac{\mu_0 ir}{2\pi R^2} \)
(E)\( \frac{\mu_0 iR}{2\pi r^2} \)

16. Which one describes the Faraday's law?(A)\( \oint \vec{E} \cdot d\vec{s} = -\frac{d\Phi_B}{dt} \)(B)\( \oint \vec{B} \cdot d\vec{s} = \mu_0 i \)(C)\( \oint \vec{B} \cdot d\vec{A} = 0 \)(D)\( \oint \vec{B} \cdot d\vec{s} = \mu_0\varepsilon_0\frac{d\Phi_E}{dt} \)
(E)\( \oint \vec{E} \cdot d\vec{A} = 0 \)

17. Consider a long solenoid of n turns per unit length carrying in it a current i. What is the stored energy density of this solenoid?(A)0(B)\( \frac{1}{2}\mu_0 n^2 i^2 \)(C)\( \frac{1}{2}\mu_0 n i^2 \)(D)\( \mu_0 n^2 i^2 \)
(E)\( \mu_0 n i^2 \)

18. What is the resonance angular frequency of a series RLC circuit?(A)\( \sqrt{RC} \)(B)\( \sqrt{LC} \)(C)\( \frac{1}{\sqrt{RC}} \)(D)\( \frac{1}{\sqrt{LC}} \)
(E)\( \sqrt{\frac{R}{LC}} \)

19. A light incident from material 1 with index of refraction, \( n_1 \), into material 2 with index of refraction, \( n_2 \). Assuming that \( n_1 ＞ n_2 \). What is the Brewster angle?(A)\( \sin^{-1} n_1 \)(B)\( \sin^{-1} n_2 \)(C)\( \tan^{-1} n_1 \)(D)\( \tan^{-1} n_2 \)
(E)\( \tan^{-1}\frac{n_2}{n_1} \)

20. A single-slit of width a is illuminated by a light of wavelength. For what value of a will the first minimum appear at \( \theta \)?(A)\( \frac{1}{2}\lambda\sin\theta \)(B)\( \lambda\sin\theta \)(C)\( \frac{\lambda}{2\sin\theta} \)(D)\( \frac{\lambda}{\sin\theta} \)
(E)\( \frac{3\lambda}{2\sin\theta} \)