Question

Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface?
The collision is elastic.

A. All of the initial kinetic energy of the less-massive object is lost.
B. The momentum of the objects that are stuck together has a smaller magnitude than the initial momentum of the less massive object.
C. The speed of the objects that are stuck together will be less than the initial speed of the less-massive object.
D. The direction of motion of the objects that are stuck together depends on whether the hit is a head on collision.

Answer 1

Answer:

C. The initial momentum should be equal to the final momentum due to the conservation of momentum.

$P_{initial} = mv_0\\P_{final} = (M+m)v_1\\v_1 = \frac{m}{M+m}v_0$

Since m/(M+m) < 1, v_1 > v_0.

Explanation:

Wrong -> A. Since the smaller particle still moves after the collision, it has a kinetic energy.

Wrong -> B. The total initial momentum is equal to the momentum of the smaller particle. Therefore, the momentum of the objects that stuck together is equal to that of the smaller object.

Wrong -> D. Since the bigger object is initially at rest and the surface is frictionless, the direction of motion will be the same as the direction of the smaller particle.