Question

A ball of mass ${}^{\prime }{m}^{\prime }$ moves towards a wall with a velocity ${}^{\prime }{u}^{\prime }$, the direction of motion making an angle $\theta$ with the surface of the wall and rebounds with the same period. The change in momentum of the ball during the collision is:

• A. $2musin$$\theta$ towards the wall
• B. $2musin$$\theta$ away from the wall
• C. $2mucos$$\theta$ towards the wall
• D. $2mucos$$\theta$ away from the wall

Answer 1

Answer: (B)

$2musin$$\theta$ away from the wall

As the ball hits the wall at an angle and rebounds, there is a change in the momentum only along the direction perpendicular to the wall. The change along the wall is zero. In diagram ${\overrightarrow{p}}_1$ and ${\overrightarrow{p}}_2$ is the momentum before and after the collision with wall.
Since , the angle with the wall is $\theta$, the change is only in $sin\theta$ component, which is across ${\overrightarrow{F}}_{wall}$.
Change in momentum$=m[usin\theta -(-usin\theta \left)\right]=2musin\theta$ away from the wall, as the final velocity is away from the wall.