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Q.

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

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a

Both (a) and (b) are correct

b

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

c

Both (a) and (b) are wrong

d

the impulse is $\overset{}{} \pm m (5 \hat{i} + \hat{j})$

answer is D.

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Detailed Solution

$\overset{}{} m (3 \hat{i} + 2 \hat{j}) = m (- 2 \hat{i} + \hat{j}) + M v (Put M = 13 m) ∴ v = \frac{(5 \hat{i} + \hat{j})}{13} J_{m} = P_{f} - P_{i} of m = [(- 2 \hat{i} + \hat{j}) - (3 \hat{i} + 2 \hat{j})] - m (5 \hat{i} + \hat{j}) ∴ J_{M} = + m (5 \hat{i} + \hat{j})$

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