7. What is the approximate minimum diameter of a focused spot for a laser beam with a wavelength of 0.5 µm?
(A) 0.005 μm
(B) 0.05 μm
(C) 0.5 µm
(D) 0.1 µm
(E) 1 μm 

3. A particle of mass m moves in a circular path of radius R under the influence of a central potential U(r)=k/r² where k is a constant. What is the Lagrangian of the system in terms of polar coordinates with angular displacement θ? (A)(B) (C) (D)(E)

4. A rigid body rotates about a fixed axis with an angular velocity ω. The body consists of two particles, each of mass m, at distances r₁ and r₂ from the axis. What is the total kinetic energy of the system? (A) (B) ½m(ωr₁)² + ½m(ωr₂)² (C) (D)(E) mω(r₁ + r₂) 

5. A source of sound moves towards a stationary observer at speed v, emitting a frequency f₀. If the speed of sound is c, what frequency does the observer hear? (A) f₀ (B) f₀c/(c-v) (C) f₀c/(c+v) (D) f₀(c-v)/c (E) f₀(c+v)/c

6. Unpolarized light passes through two polarizing filters. The first is oriented vertically, and the second is rotated 30° relative to the first. What fraction of the intensity of the light that passes through the first filter also passes through the second filter? (A) 1/2 (B) 3/4 (C)(D) 3/8 (E)

8. During an adiabatic compression of an ideal gas, which of the following statements is true? (A) The temperature of the gas decreases. (B) The pressure of the gas remains constant. (C) The internal energy of the gas decreases. (D) The temperature of the gas increases. (E) The entropy of the gas increases. 

9. An ideal gas undergoes an isothermal expansion, doubling its volume. If the initial pressure is P₀ and the initial volume is V₀, calculate the final pressure of the gas. (A) P₀/4 (B) P₀/2 (C) P₀ (D) 2P₀ (E) 0 

10. A cylinder containing a gas at 400 K is fitted with a piston, allowing the gas to do 200 J of work during an isobaric expansion. Calculate the change in internal energy if 50 J of heat is lost to the surroundings. (A) 150 J (B) -50 J (C) -250 J (D) 50 J (E) 200 J

11. What is the entropy change when 18 grams of water at 100°C and 1 atm is completely converted to steam at the same temperature and pressure? (The latent heat of vaporization of water is 2260 kJ/kg) (A) 12.6 J/K (B) 25.2 J/K (C) 75.6 J/K (D) 109.2 J/K (E) 252.0 J/K 

12. A point charge q is placed at the center of a non-conducting spherical shell of inner radius r₁ and outer radius r₂. What is the electric field at a distance r from the center where r₁<r<r₂? (A) (B)(C) 0 (D)(E)

13. A rectangular loop of wire lies in the xy-plane with current I flowing in a clockwise direction when viewed from the positive z-axis. The loop dimensions are a along the x-axis and b along the y-axis. A uniform magnetic field B₀ along the positive z-direction is applied in the region. Using Ampere's Law, determine the net magnetic field at the center of the loop. (A) B₀ along the positive z-direction (B) B₀ along the positive x-direction (C) B₀ along the negative y-direction (D) B₀ along the negative z-direction (E) 0