6. Two far apart charged metal spheres of radius R₁ and R₂ are connected by a long wire in electrostatic equilibrium. The electric potentials and the surface charge densities on them are V₁, V₂ and σ₁, σ₂, respectively. Choose the correct statement.
(A) V₁ ＞ V₂, σ₁ ＞ σ₂
(B) V₁ ＜ V₂, σ₁ ＜ σ₂
(C)
(D) V₁ = V₂, R₁σ₁ = R₂σ₂
(E) R₁V₁ = R₂V₂, σ₁ = σ₂

1. As shown in Fig. 1, the mass of block 1 is m₁, and the mass of block 2 is m₂, where m₁ ＜ m₂. The radius and mass of the frictionless pulley are R and M, respectively, so the rotational inertia is MR²/2. The pulley is fastened to the ceiling. The massless cord cannot slip on the pulley. The system is released from rest. The torque τ on the pulley and the tension T₂ are (A) (B) (C) (D)(E)

2. For the same system shown in Fig. 1, which statement shown below is correct? (A) The quantities of the acceleration of block 1 and block 2 are different. (B) The system's center of mass won't move at all. (C) T₁ is smaller than T₂. (D) The system's angular momentum will be conserved. (E) The system's kinetic energy is equal to the sum of the kinetic energies of m₁ and m₂.

3. A particle of mass m located at a distance d from one end of a uniform rod, as in Fig. 2. The mass of the rod is M, and the length is L. Find the "escape speed" of the particle. (A)(B)(C) (D) (E)

4. A long straight wire is in the plane of a loop wire, as shown in Fig. 3. The straight wire initially carries no current. While the current i is smoothly increasing from zero, the current in the rectangle loop is (A) zero (B) clockwise (C) counterclockwise (D) clockwise in the left side and counterclockwise in the right side (E) counterclockwise in the left side and clockwise in the right side.

5. The current i is from left to right in the conductor as shown in Fig. 4. The magnetic field B is upward and point S is at a higher potential than point T. The charge carriers are (A) positive (B) neutral (C) negative (D) absent (E) unable to be identified

7. The resistivity of pure silicon at 20°C is 2.5×10³ Ω·m, and the temperature coefficient of resistivity is −70×10⁻³ K⁻¹. What's the resistivity of pure silicon at 30°C? (A) 1.8×10³ Ω·m (B) −4.25×10³ Ω·m (C) −0.75×10³ Ω·m (D) 4.25×10³ Ω·m (E) 0.75×10³ Ω·m

8. As the circuit in Fig. 5, the resistance of each resistor is 2 Ω. The currents i₁, i₂ through the batteries are (A) +0.66 A, −0.66 A (B) +0.5 A, 0 A (C) +1.0 A, +0.5 A (D) +0.66 A, −0.5 A (E) −0.66 A, 0 A

9. The electric flux of E = (2,3,6) N/C through one 2.0 m² area on xy plane is (A) 6 N·m²/C (B) 4 N·m²/C (C) 9 N·m²/C (D) 3 N·m²/C (E) 12 N·m²/C

10. In an "adiabatic" process, which statement is correct about the heat Q, the work done W, and the internal energy ΔEint in an ideal gas system? (A) Q ＞ 0, W ＞ 0, ΔEint = 0 (B) Q ＜ 0, W ＞ 0, ΔEint = 0 (C) Q = 0, W = ΔEint (D) Q = 0, W = −ΔEint (E) None in above.

11. As shown in Fig. 6, an electrical hot plate inside a chamber generates heat in a rate of P = 100 W. One of the chamber walls is made of copper with thermal conductivity kCu = 401 W/m·K. The other walls are fiber wool which are nearly thermal insulated with kfiber = 0.048 W/m·K. The copper wall thickness is 3 mm, and the cross-section area is 0.1 cm². If the temperature outside the chamber is TL = 20 °C, in condition of thermal equilibrium, the temperature TH inside the chamber is (A) 24.8 °C (B) 34.8 °C (C) 58.8 °C (D) 84.8 °C (E) 94.8 °C

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