At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the acceleration of the center of mass of the two-ball system is:
A) 0.25g
B) 0.50g
C) 0.75g
D) g
E) g/0.75

Question

Quizplus · Accepted Answer

The center of mass of a system of objects is given by the weighted average of their positions, where the weights are the masses of the objects. In this case, the center of mass will lie closer to the ball with the larger mass, since it has more weight.

At the moment the balls are released, the center of mass will be at a height of (0.50*25)/(0.50+0.25) = 16.67 m above the ground, closer to the 0.50 kg ball.

Over the next 2.0 s, the 0.50-kg ball will accelerate downward under the influence of gravity, while the 0.25-kg ball will move upward and slow down due to the force of gravity pulling it down. However, the acceleration of the center of mass will be determined solely by the external forces acting on the system.

The only external force acting on the system is the force of gravity, which acts equally on both balls. Therefore, the center of mass will accelerate downward at the same rate as the free-falling 0.50-kg ball, which is g = 9.8 m/s^2.

Thus, the answer is D) g.

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