19. Suppose Bohr had chosen the potential energy of the electron in the hydrogen atom to be V = 0 when the electron is in the orbit with n = 1. He could do this by

(A) choosing n = 1 for the orbit where the kinetic energy of the electron is zero.

(B) adding a constant 13.6 eV to the potential energy for all values of n.

(C) adding a constant 27.2 eV to the potential energy for all values of n.

(D) subtracting a constant 13.6 eV from the potential energy for all values of n.

(E) subtracting a constant 27.2 eV from the potential energy for all values of n.

4. A 10-kg block on a horizontal, frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position? (A) 0.85 m/s (B) 0.95 m/s (C) 0.73 m/s (D) 0.64 m/s (E) 0.51 m/s

5. Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released. Which statement is correct? (A) Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point. (B) Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point. (C) Masses A and B will travel equal distances between their highest and lowest points. (D) More work was done on mass A by the extending force than on mass B by the compressing force. (E) The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.

6. A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth, horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg·m². The cord does not slip on the pulley. What is the magnitude of the acceleration of m? (A) 2.4 m/s² (B) 3.8 m/s² (C) 4.2 m/s² (D) 5.2 m/s² (E) 1.1 m/s²

7. Aluminum Rod #1 has a length L and a diameter d. Aluminum Rod #2 has a length 2L and a diameter 2d. If Rod #1 is under tension T and Rod #2 is under tension 2T, how do the changes in length of the two rods compare? (A) They are the same. (B) Rod #1 has double the change in length that Rod #2 has. (C) Rod #2 has double the change in length that Rod #1 has. (D) Rod #1 has quadruple the change in length that Rod #2 has. (E) Rod #2 has quadruple the change in length that Rod #1 has.

8. A large water storage container is filled to a depth of 3.0 m. The volume above the water is filled with air. In order to pump the water from the container, the air pressure in the container is increased by 3.0 × 10⁵ N/m². What happens to the pressure in the water at a depth of 1.0 m when the air pressure is increased? (A) Nothing, it is still at a depth of 1.0 m and the pressure in the water depends only on the depth. (B) It increases by 1.0 × 10⁵ N/m², since it is at 1/3 the depth of the water. (C) It increases by 2.0 × 10⁵ N/m², since it is at 2/3 the depth from the bottom of the container. (D) It increases by 3.0 × 10⁵ N/m². (E) It increases by 3.0 × 10⁵ N/m² + 9.8 × 10³ N/m² since it is 1.0 m deep in the water.

9. To transmit four times as much energy per unit time along a string, you can (A) double the frequency. (B) double the amplitude. (C) increase the tension by a factor of 16. (D) do any one of the above. (E) do only ( A ) or ( B ) above.

10. A 100-g cube of ice is heated from −120°C to +120°C. In which of the following processes is the greatest amount of energy absorbed by this material? (A) warming ice to the melting point (B) melting the ice to become water (C) warming the resulting water (D) heating the steam (E) vaporizing the water to become steam

11. Two tanks of gas, one of hydrogen, H₂, and one of helium, He, contain equal numbers of moles of gas. The gram-molecular mass of He is twice that of H₂. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion? (A) The total internal energy of the hydrogen is the same as that of the helium. (B) The total internal energy of the hydrogen is 1.4 times that of the helium. (C) The total internal energy of the helium is 1.4 times that of the hydrogen. (D) The total internal energy of the hydrogen is 1.67 times that of the helium. (E) The total internal energy of the helium is 1.67 times that of the hydrogen.

12. For the same temperature increase in a system, the change in entropy, ΔS, is largest in a reversible (A) constant-volume process. (B) constant-pressure process. (C) adiabatic process. (D) process in which no heat is transferred. (E) process in which no work is performed.

13. Charge of uniform density (20 nC/m²) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m². Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces. (A) 3.3 kN/C (B) 1.1 kN/C (C) 2.7 kN/C (D) 5.4 kN/C (E) 4.5 kN/C

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