A particle of mass ‘m’ moving with a velocity $(3 \overset{\land}{i} + 2 \overset{\land}{j})$ m/s, collides with a stationary mass ‘M’ and finally m moves with velocity $(- 2 \overset{\land}{i} + \overset{\land}{j})$ m/s. If $\frac{m}{M} = \frac{1}{13}$ , the velocity of the M after collision is,

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$(5 \overset{\land}{i} + \overset{\land}{j})$ m/s

$(5 \overset{\land}{i} - \overset{\land}{j})$ m/s

$(\frac{5 \overset{\land}{i}}{13} - \frac{\overset{\land}{j}}{13})$ m/s

$(\frac{5 \overset{\land}{i}}{13} + \frac{\overset{\land}{j}}{13})$ m/s

answer is D.

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Detailed Solution

$A p p l y i n g l a w o f c o n s e r v a t i o n o f l i n e a r m o m e n t u m l e t f i n a l v e l o c i t y o f M b e V m (3 \overset{\land}{i} + 2 \overset{\land}{j}) + 0 = m (- 2 \overset{\land}{i} + \overset{\land}{j}) + M \cdot V$
$\Rightarrow m (3 \overset{\land}{i} + 2 \overset{\land}{j} + 2 \overset{\land}{i} - \overset{\land}{j}) = M \cdot V; V = \frac{m}{M} (5 \overset{\land}{i} + \overset{\land}{j})$
$∴ V = \frac{1}{13} (5 \overset{\land}{i} + \overset{\land}{j})$ m/s
$\Rightarrow V = (\frac{5 \overset{\land}{i}}{13} + \frac{\overset{\land}{j}}{13}) m s^{- 1} = f i n a l v e l o c i t y o f M$