A ball of mass 'm' having velocity 'u' hits a rigid wall. If there is no change in the velocity of the ball after reflection from the wall, then what will be change in the Momentum of the ball.

Question

Accepted Answer

The correct option is (3): -2mu

Let's break down this problem on momentum change during a collision. Momentum, symbolized as $p$, is a vector quantity defined as the product of an object's mass ($m$) and its velocity ($v$), i.e., $p = mv$. It has both magnitude and direction.

When a ball of mass 'm' hits a rigid wall with velocity 'u', we can define its initial momentum. Since momentum is a vector, we need to consider direction. Let's assume the initial direction of the ball towards the wall is positive.
So, Initial momentum ($p\_i$) = $m 	imes (+u) = +mu$.

The problem states that there is no change in the velocity of the ball after reflection from the wall. This means the magnitude of the velocity remains 'u', but its direction reverses as it bounces back from the rigid wall.
Therefore, the final velocity of the ball after reflection will be $-u$.
So, Final momentum ($p\_f$) = $m 	imes (-u) = -mu$.

The change in momentum ($\Delta p$) is calculated as the final momentum minus the initial momentum:
$\Delta p = p\_f - p\_i$
$\Delta p = (-mu) - (+mu)$
$\Delta p = -mu - mu$
$\Delta p = -2mu$

The negative sign indicates that the change in momentum is in the direction opposite to the initial velocity. Thus, the change in momentum of the ball is $-2mu$. This result highlights the vector nature of momentum and how a change in direction significantly affects its value.

The incorrect option is (1): O
This option would imply no change in momentum, which is incorrect because the ball's direction of motion has reversed, leading to a change in its momentum vector. A change in velocity (even if only in direction) results in a change in momentum.

The incorrect option is (2): -mu
This option represents the final momentum of the ball, not the change in momentum. The change is the difference between the final and initial momenta.

The incorrect option is (4): -4mu
This value is not derived from the principles of momentum change in this scenario. It suggests an incorrect calculation of either initial, final, or the difference between them.