15. A wooden rod of uniform cross section and of length l is hinged at the bottom of a tank which is filled with water to a height h = l/3, as shown in right figure. If the density of wood is 0.45 g/cm³, find the angle θ from the vertical at which the rod is in equilibrium.

(A) θ = 60°
(B) θ = 30°
(C) θ = 45°
(D) θ = 37°
(E) θ = 53°

16. The temperatures TC of the cold reservoirs and the temperatures TH of the hot reservoirs for four Carnot heat engines are engine 1: TC = 400 K and TH = 500 K; engine 2: TC = 500 K and TH = 600 K; engine 3: TC = 400 K and TH = 600 K; engine 4: TC = 600 K and TH = 800 K. Rank these engines according to their efficiencies, least to greatest (A) 1→2→3→4 (B) 1 and 2 tie, then 3 and 4 tie (C) 2→1→3→4 (D) 1→2→4→3 (E) 2→1→4→3

17. A source at rest emits light of wavelength 500 nm. When it is moving at 0.90 C (C is light speed) away from an observer, the observer detects light of wavelength: (A) 26 nm (B) 115 nm (C) 500 nm (D) 2200 nm (E) 9500 nm

18. Light with an intensity of 1 kW/m² falls normally on a surface with an area of 1 cm² and is completely absorbed. The force of the radiation on the surface is: (A) 3.3 × 10⁻¹¹ N (B) 1.7 × 10⁻¹⁰ N (C) 3.3 × 10⁻¹⁰ N (D) 6.7 × 10⁻¹⁰ N (E) 1.0 × 10⁻⁴ N

19. The stopping potential for electrons ejected by 6.8 × 10¹⁴-Hz electromagnetic radiation incident on a certain sample is 1.8 V. The kinetic energy of the most energetic electrons ejected and the work function of the sample, respectively, are: (A) 1.8 eV, 2.8 eV (B) 1.8 eV, 1.0 eV (C) 1.8 eV, 4.6 eV (D) 2.8 eV, 1.0 eV (E) 1.0 eV, 4.6 eV

20. The right figure shows the energy levels for an electron in a finite potential energy well. If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon? (A) 6.0 nm (B) 5.7 nm (C) 5.3 nm (D) 3.0 nm (E) 2.3 nm

1. The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (−5.00 × 10⁷) t² + (3.00 × 10⁵) t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero. Which answers are correct in the followings? (A) The length of time the bullet is accelerated is 6.00×10⁻³ s. (B) The length of time the bullet is accelerated is 3.00×10⁻³ s. (C) The length of time the bullet is accelerated is 2.00×10⁻³ s. (D) The speed at which the bullet leaves the barrel is 900 m/s. (E) The speed at which the bullet leaves the barrel is 450 m/s.

2. Right figure shows a reversible cycle through which 1 mol of a monatomic ideal gas is taken. Assume p = 2p₀, V = 2V₀, p₀ = 1.01 × 10⁵ Pa, and V₀ = 0.0225 m³. (A) The work done during the cycle is 2.27 kJ. (B) The energy added as heat during stroke abc is 14.8 kJ. (C) The efficiency of the cycle is 0.217. (D) The efficiency of a Carnot engine operating between the highest and lowest temperatures that occur in the cycle is 0.25. (E) The efficiency of Carnot engine is thus greater than the efficiency of the cycle showed in the right figure.

3. In A. J. Dempster's mass spectrometer as shown in right figure, two isotopes with masses m₁ and m₂ are accelerated from rest by a potential difference V₀. They then enter a uniform field B normal to the magnetic field lines. (Assume both isotopes have the same charge q) (A) Both kinetic energies of the accelerated particles are qV₀ (B) The speed of isotope with m₁ is v₁ = (qV₀/m₁)1/2(C) The radius of the path in the magnetic field for the isotope with m₂ is r₂ = (m₂V₀/qB²)1/2 (D) r₁/r₂ = (m₁/m₂)1/2(E) r₁/r₂ = (m₂/m₁)1/2

4. A particle encounters a position-dependent potential energy as shown in the figure to the right. Choose the CORRECT statement(s): (A) The maximum kinetic energy of the particle is 4×10⁻²⁰ J when its total energy is E₁. (B) The maximum kinetic energy of the particle is 4×10⁻²⁰ J when its total energy is E₂. (C) The particle experiences no force at r = 2×10⁻¹⁰ m when its total energy is E₁. (D) The particle experiences no force at r = 2×10⁻¹⁰ m when its total energy is E₂. (E) The particle experiences a maximum attractive force at r = 4×10⁻¹⁰ m when its total energy is E₂.

1. A block with mass m is vertically attached between two ideal springs with the force constant k and vertically oscillates (Fig. 1). What is the angular frequency? (A) (B)(C) (D) (E)

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