Question

A rigid ball of mass m strikes a rigid wall at ${60}^0$ 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. mV
• B. 2 mV
• C. $\frac{mV}{2}$
• D. $\frac{mV}{3}$

Answer 1

Answer: (A)

mV

Given, $P_i=P_f=mV$
Change in momentum of the ball = ${\overline{P}}_f-{\overline{P}}_i$
=$(-P_{fx}\hat{i}-P_{fy}\hat{j})-(P_{ix}\hat{i}-P_{iy}\hat{j})$

=$-\hat{i}(P_{fx}+P_{ix})-\hat{j}(P_{fy}-P_{iy})$

=$-2P_{ix}\hat{i}=-mV\hat{i}$ $[P_{fy}-P_{iy}=0]$
Impulse imparted by the wall = change in the momentum of the ball = mV.