Question

A ball with initial momentum $P$ collides with rigid wall elastically. If $P^{{}^{\prime }}$ be its momentum after collision then:

• A. $P^{{}^{\prime }}=P$
• B. $P^{{}^{\prime }}=-P$
• C. $P^{{}^{\prime }}=2P$
• D. $P^{{}^{\prime }}=-2P$

Answer 1

The correct option is B $P^{{}^{\prime }}=-P$

In an elastic collision, when an object collides with an object with its mass much greater greater, the heavier body remains practically at rest. In this example, the rigid wall plays the role of the heavier object. Let the velocity of ball be v.
$v_2-(-v_1)=e{u}_1-u_2$($v_2$ and $v_1$ are in opposite direction)
But for elastic collision, $e=1$ and the velocity of wall remains zero. Thus we get
$v_2=-v_1$
or
$m{v}_2=-m{v}_1$
or
$P^{\prime }=-P$