9. A conducting sphere is charged such that the electric potential on its surface is 100 volt (V) (relative to infinity). If the radius of the sphere were doubled, but the total charge on the sphere remained the same, what would be the new potential on the surface relative to infinity?
(A) 400 V
(B) 200 V
(C) 100 V
(D) 50 V
(E) 25 V

8. A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity? (A) 25 V (B) 50 V (C) 100 V (D) 200 V (E) 400 V

10. What is the maximum theoretical efficiency of a Carnot heat engine operating between a heat source at 500 K and a heat sink at 300 K? (A) 20% (B) 30% (C) 40% (D) 50% (E) 60%

11. A musician can identify a 2 kilo-Hz pure tone in 8 milli-seconds. How many periods of the sound wave is this? (A) 16 (B) 20 (C) 24 (D) 28 (E) 30

12. A pitcher throws a ball of mass m at an angle such that the ball can travel a maximum distance R. Find the initial kinetic energy K0 of the ball. The gravitational acceleration is denoted as g. (Ignore the height of the pitcher) (A) K0=2mgR (B) K0=mgR (C) K0=(1/2) mgR (D) K0=(1/4) mgR (E) K0=(1/8) mgR

13. The human heart acts as a biological pump, generating pressure to circulate blood throughout the body. The human heart could pump about 80 cm3 of blood per contraction, and this quantity is called the stroke volume. Assume that mean arterial pressure is 120 mm-Hg and the heart beat rate is 70/min. Calculate the average power output of the heart in watt (W). [1 atm=760 mm-Hg= 1.013×105 Pa] (A) 2.7 W (B) 1.5 W (C) 3.2 W (D) 0.8 W (E) 4.2 W

14. Babies are naturally more sensitive to some pitched sounds differently than adults. This is due to the difference in the length of the ear canal. Calculate the fundamental resonant frequency f1 of the 1.27 cm long ear canal of a baby. Calculate the fundamental resonant frequency f2 of the 2.6 cm long ear canal of an adult. The answer is written in the form (f1, f2). The speed of sound in air is 344 m/s. (A) (7343 Hz, 4370 Hz) (B) (3543 Hz, 6880 Hz) (C) (6771 Hz, 3307 Hz) (D) (3443 Hz, 7698 Hz) (E) (9371 Hz, 5890 Hz)

15. A hearing aid increases the sound intensity level by 20 decibels (dB). By what factor does this increase the actual sound intensity? (A) 800 (B) 400 (C) 200 (D) 100 (E) 2

16. Which reagent can reduce 2-butanone to n-butane? (A) NaBH4 (B) LiAlH4 (C) PCC (D) Zn(Hg), HCl (E) KMnO4

17. The ground state term symbol for the neutral oxygen atom (O) is relevant to discussions of reactive oxygen species or atomic oxygen in biochemical contexts. What is the ground state term symbol for O? (A) 1S (B) 1P (C) 1D (D) 3P (E) 3D

18. Which statement about the Hartree-Fock (HF) method is correct? (A) The HF method gives the exact electronic energy because it includes full electron correlation. (B) The HF method approximates the many-electron wavefunction as a single Slater determinant, enforcing antisymmetry. (C) The HF method treats electron-electron repulsion only as a constant and ignores exchange effects. (D) In the HF method, the orbitals are fixed and never optimized; only the total energy is minimized. (E) The HF method is a semi-empirical method because it requires experimental parameters.

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