First slide

The steps in collision

Question

A particle of mass m kg moving with a velocity $(3 \hat{i} + 2 \hat{j}) {ms}^{- 1}$ collides with a stationary body of mass M kg and finally moves with a velocity $(- 2 \hat{i} + \hat{j}) {ms}^{- 1}$ . If $\frac{m}{M} = \frac{1}{13},$ then

Moderate

A

the impulse is $\pm m (5 \hat{i} + \hat{j}) kg . {ms}^{- 1}$
B

the velocity of the M is $\frac{1}{13} (5 \hat{i} + \hat{j}) {ms}^{- 1}$
C

Both (a) and (b) are wrong
D

Both (a) and (b) are correct

Solution

$m (3 \hat{i} + 2 \hat{j}) = m (- 2 \hat{i} + \hat{j}) + M v$
$∴$ $v = \frac{(5 \hat{i} + \hat{j})}{13} {ms}^{- 1}$ (put, M=13m)
Impulse, $J_{m} = p_{f} - p_{i} = \pm m [(- 2 \hat{i} + \hat{j}) - (3 \hat{i} + 2 \hat{j})]$
$∴$ $J_{m} = \pm m (5 \hat{i} + \hat{j}) kg \cdot {ms}^{- 1}$

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