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. $2m$ $V$
• C. $\frac{mV}{2}$
• D. $\frac{mV}{3}$

Answer 1

Answer: (A)

Given, $p_i$ $=p_f$ $=mV$
Change in momentum of the ball = ${\vec{p}}_f$ $-{\vec{p}}_i$

$=\left(-p_{fx}\hat{i}-p_{fy}\hat{j}\right)$ $-\left(p_{ix}\hat{i}-p_{iy}\hat{j}\right)$
$=-\hat{i}\left(p_{fx}+p_{ix}\right)-\hat{j}$ $\left(p_{fx}-p_{iy}\right)$
$=-2p_{ix}\hat{i}=-mV\hat{i}$ $\left[\because p_{fy}-p_{iy}=0\right]$
Here, $p_{ix}=p_{fx}$ $=p_{i}cos60^{\circ }$ $=\frac{mV}{2}$
$\because$ Impulse imparted by the wall = change in the momentum of the ball = $m$ $V$