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)\( \frac{\mu_0 iR}{2\pi r^2} \)

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