Question

A rigid ball of mass $m$ strikes a wall at ${60}^{\circ }$ and gets reflected without loss of speed as shown in figure. The value of impulse imparted by the wall on the ball will be:

• A. $mv$
• B. $2mv$
• C. $\frac{mv}{2}$
• D. $\frac{mv}{3}$

Answer 1

The correct option is A $mv$

The component of velocity has changed along $x-$direction as shown in figure, hence momentum of ball has changed along the $x-$ direction after receiving impulse from the wall.


$\Rightarrow \text{Net impulse in x- direction}=\Delta P_x$
$J_x=(P_x{)}_f-(P_x{)}_i=\left(mv\cos {60}^{\circ }\hat{i}\right)-(-mv\cos {60}^{\circ }\hat{i})$
$\Rightarrow J_x=2mv\cos {60}^{\circ }\hat{i}=2mv\times \frac{1}{2}=mv\hat{i}$
$\therefore |J_x|=mv$
Hence wall has exerted impulse of value $mv$ in a direction normal to wall.