A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground.The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is A)0. B) . C) . D)1 E) .

Question

Quizplus · Accepted Answer

The kinetic energy of the ball just before it hits the ground is given by (1/2)mv^2, where m is the mass of the ball and v is its velocity. The kinetic energy of the Earth is given by (1/2)MEv^2, where ME is the mass of the Earth. Since the ball is much lighter than the Earth, it acquires much more kinetic energy than the Earth does. The ratio of the kinetic energy of the Earth to that of the ball is (1/2)MEv^2 / (1/2)mv^2 = (ME/m), which is much greater than 1. Therefore, the correct answer is C.

A Ball of Mass MB Is Released from Rest and Acquires

A Ball of Mass M_B Is Released from Rest and Acquires