A system of two blocks $A$ and $B$ are connected by an inextensible massless string as shown in the figure. The pulley is massless and frictionless. Initially the system is at rest. A bullet of mass $m$ hits the block $B$ with speed $u$ and get embedded into it. The impulse imparted by tension to the block of mass $3 m$ is:

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$\frac{5 m u}{4}$

$\frac{2 m u}{5}$

$\frac{4 m u}{5}$

$\frac{3 m u}{5}$

answer is D.

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Detailed Solution

For block $A \int T d t = 3 m v - 0$

For block B+bullet system $- \int T d t = 2 m v - m u$

$v = \frac{u}{5}$

the impulse imparted by tension force to the block of mass 3m is $3 m v = \frac{3 m u}{5}$

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