Four small blocks are placed on smooth horizontal surface and lie on same horizontal straight line. The blocks have masses $m_{1} = m_{2} = m_{4} = m$ and $m_{3} = 2 m .$ Blocks 1, 3, and 4 are initially stationary, while block 2 is initially moving towards block 3 at speed $v = 9 m / s .$ Assuming that collisions involving block 1 or block 4 are perfectly inelastic, while collision between blocks 2 and 3 is perfectly elastic, then the final speed of block 4 in $m / s$ is_____

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answer is 4.

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Detailed Solution

Let velocities of block 2 and block 3 be $v_{2}$ and $v_{3}$ towards right.

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from conservation of momentum
$m v = m v_{2} + 2 m v_{3} ........ (1)$
and from equation of restitution
$v_{3} - v_{2} = v ........ (2)$
from (1) and (2)
$v_{3} = \frac{2 v}{3}$
Since collision between 3 and 4 is inelastic.
final velocities of 3 and 4 are $v_{4} = \frac{2 m \frac{2 v}{3}}{m + 2 m} = \frac{4 v}{9}$