A rigid ball of mass 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 [2016]

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Solution

Q.
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 [2016]

1 $m V$

2 $2 m V$

3 $\frac{m V}{2}$

4 $\frac{m V}{3}$

Ans.
(1)

Given, $p_{i} = p_{f} = m V$

Change in momentum of the ball = ${\vec{p}}_{f} - {\vec{p}}_{i}$

$= - (p_{f x} \hat{i} - p_{f y} \hat{j}) - (p_{i x} \hat{i} - p_{i y} \hat{j})$

$= - \hat{i} (p_{f x} + p_{i x}) - \hat{j} (p_{f y} - p_{i y})$

$= - 2 p_{i x} \hat{i} - 0 \hat{j} = - m V \hat{i}$

Here, $p_{i x} = p_{f x} = p_{i} \cos 60 ° = \frac{m V}{2}$

$∵$ Impulse imparted by the wall = change in the momentum of the ball = $m V$

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