5. Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?
(A) 4 m
(B) 5 m
(C) 6 m
(D) 10 m
(E) none of above； need to know the forces they exert.

1. A particle travels with constant speed v around a circle of radius R. For an interval in which it travels 5/6 of the way around the circle (i.e., through 300°), the ratio of the magnitude of its average acceleration to the magnitude of its instantaneous acceleration is: (A) 1/6 (B) 3√3/10π (C) 3/5π (D) √3/10 (E) 6/5π.

2. In the right figure, with about what steady force must the man pull on the rope to achieve an upward acceleration of 0.50 m/s2? The man has a mass of70 kg and the chair has a mass of 10 kg. (A) 370 N (B) 410 N (C) 820 N (D) 740 N (E) 390 N.

3. Two objects with masses, m1 and m2, have the same kinetic energy and are both moving to the right. The same constant force is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is: (A) 1:4 (B) 4:1 (C) 1:2 (D) 2:1 (E) 1:1.

4. The potential energy of a 0.20-kg particle moving along the x axis under a conservative force field is: U(x) =(8.0J/m²)x² - (2.0J/m²)x⁴ When the particle is at x = 1.0 m, its acceleration is: (A) 0 î (B) -8 m/s² î (C) 8 m/s² î (D) -40 m/s² î (E) 40 m/s² î.

6. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR². A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is: (A) (2/5)MR² (B) 9MR² (C) 16MR² (D) 47/5MR² (E) (82/5)MR².

7. A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then: (A) mRv/(I-mR²) (B) mRv/(I+mR²) (C) mRv/I (D) 2mRv/I (E) v/R.

8. The amplitude of any oscillator can be doubled by: (A) doubling both the initial displacement and the initial speed (B) doubling only the initial speed (C) doubling only the initial displacement (D) doubling the initial displacement and halving the initial speed (E) doubling the initial speed and halving the initial displacement.

9. The displacement of a string carrying a traveling sinusoidal wave is given by y(x,t) = (kx – wt – φ). At time t = 0 the point at x = 0 has velocity v0 and displacement y0. The phase constant φ is given by tan (A) ν0/ωγ0 (B)ων0/γ0 (C) wy0/v0 (D) y0/ων0 (E) 0.

10. Consider the following processes: The temperature of two identical gases are increased from the same initial temperature to the same final temperature. Reversible processes are used. For gas A the process is carried out at constant volume while for gas B it is carried out at constant pressure. The change in entropy: (A) is greater for A only if the initial pressure of gas A is higher than gas B (B) is the same for A and B (C) is greater for A (D) is greater for B (E) can't be compared without more information.

11. Two identical conducting spheres, "1" and "2", carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere, "3", is uncharged. Sphere "3" is first touched to "1", then to "2", and finally removed. As a result, the electrostatic force between "1" and "2", which was originally F, becomes: (A) F/2 (B) F/4 (C) F/18 (D) 3F/8 (E) 0.