Question

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

• A. $m$ $V$
• B. $2 \,m$ $V$
• C. $\frac{m V} {2}$
• D. $\frac{m V}{3}$

Answer 1

The Correct Option is A

Given, $p_{i}$ $=p_{f}$ $=m V$
Change in momentum of the ball = $\vec{p}_{f}$ $-\vec{p}_{i}$
$=\left(-p_{fx} \hat{i}-p_{fy} \hat{j}\right)$ $-\left(p_{ix} \hat{i}-p_{iy} \hat{j}\right)$
$=-\hat{i} \left(p_{fx}+p_{ix}\right)-\hat{j}$ $ \left(p_{fx}-p_{iy}\right)$
$=-2 p_{ix} \hat{i}=-m V \hat{i}$ $\left[\because\quad p_{fy}-p_{iy}=0\right]$
Here, $p_{ix}=p_{fx}$ $=p_{i} \, cos \, 60^{\circ}$ $=\frac{m \,V}{2}$
$\because$ Impulse imparted by the wall = change in the momentum of the ball = $m$ $V$