10. Two uniform ladders, both of length L, are hinged at point A and tied together by a horizontal rope at its center. The angle between the ladders is 90 degree. The ladders have mass m₁ and m₂ respectively. Assume the floor is frictionless. Find the tension in the rope.

(A)

(B)

(C)

(D) 2m₁g + 2m₂g

(E) 0

11. One mole of real gas with interaction between molecules obeys van der Waals equation of state, (P + )(V - b) = RT. The internal energy function can be calculated to be Eint =RT - . What is Cv, the molar heat capacity at constant volume of this gas?(A)(B) (C) (D) (E)

12. A heat engine using monatomic ideal gas undergoes a cyclic process BACB, where BA is an isothermal process. In which process(es) does the gas absorb heat from the environment? (A) AC (B) AC and CB (C) AC and BA (D) BA and CB (E) All three processes

13. A cylinder has insulating walls and is divided into two parts by a frictionless insulating piston. Initially, the two parts have equal volumes V0, equal temperatures To and equal pressure P0. The gas is ideal with Cv = R, Cp = . A small heating bar is now inserted on the left part and heat is supplied slowly to the gas on the left until its pressure reaches 32P0. As a result, the left part will expand and the right part will be compressed. How much heat is supplied to the gas on the left part? (A) 32 P0V0 (B) PoVo (C) P0V0 (D) 59 P0V0 (E) 93 P0V0

14. A particle with mass m and positive charge q starts from rest at the origin under a uniform electric field in the +y-direction and a uniform magnetic field directed out of the page, so . Neglecting gravity, the particle is accelerated by the E field, but the magnetic force bends it to the right and the resulting trajectory is shown in the figure. At point P, the particle reaches its maximum height ymax. What is the velocity of the particle at point P?(A)(B) (C) (D) (E)

15. The Maxwell's equations related to static magnetic field are and . Which of the following magnetic field line illustrated in the figures clearly violates Maxwell's equation?(A)(B) (C) (D) (E)

16. Consider the n = 4 states of hydrogen, what is the minimum angle θ between its angular momentum vector and the z-axis?(A) (B)(C) (D) (E) 0

17. Two blocks (with the same mass m) connected by a spring of negligible mass are at rest on a frictionless table, as shown in the upper part of figure. The separation distance of the blocks when the spring is relaxed is L. During a time interval △t, a constant force of magnitude F is applied horizontally to the left block, moving it through a distance x₁ as shown in the lower part of figure. During this time interval, the right block moves through a distance x2. At the end of this time interval when the force is removed, what is the maximum energy could be momentarily stored in the spring?(A) F(x₁+x₂) (B) F(x₁+x₂)/2 (C) F(x₁-x₂)/2 (D) F(x₁-x₂) (E) It cannot be determined.

18. A block of mass M is attached to a spring of mass m and force constant K. What is the time period T of oscillation of the block-spring system?(A) 2π√(M/k)(B) 2π√((M/k) + √(m/k))(C) 2π√((k/M) + √(k/m))^(-1)(D) 2π√((M+m)/k)(E) 2π√((M+(m/3))/k)

19. Imagine that an ideal monatomic gas is taken from its initial state B to state D by an isobaric process, from D to A by an isochoric (i.e., isovolumetric) process, and from A back to its initial state B by an isothermal process. What is the thermal efficiency of this BDAB cycle? Note that ln2 = 0.6931 and ln10 = 2.3026.(A) 0.144(B) 0.192(C) 0.240(D) 0.288(E) None of the above

20. To explain the phenomenon of condensation of real gases to liquids, two constants A and B for different gases are introduced in the van der Waals equation of stateWhich of the following expression is correct?(A) A ＜ 0 and B ＜ 0(B) A ＞ 0 and B ＜ 0(C) A ＞ 0 and B ＞ 0(D) A ＜ 0 and B ＞ 0(E) Whether A is larger or smaller than 0 depends on gases

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