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Velocity of Separation and Approach

Four blocks o...

Question

Four blocks of masses $M_{1}, M_{2}, M_{3}$ and $M_{4}$ are placed on a smooth horizontal surface along a straight line as shown above. It is given that $M_{1} >> M_{2} >> M_{3} >> M_{4} .$ All the blocks are initially at rest. $M_{1}$ is given initial velocity $v_{0}$ towards right such that it will collide with $M_{2} .$ Consider all collisions to be perfectly elastic. The speed of $M_{4}$ after all collision are over is

A

v_{0}

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B

4

v_{0}

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C

8

v_{0}

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D

16

v_{0}

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Solution

The correct option is B 8 $v_{0}$
$M_{1}$ is very large as compared to $M_{2} .$ Hence for collision between $M_{1}$ and $M_{2}, M_{1}$ can be considered equivalent to a wall and $M_{2}$ as a small block. Thus the velocity of $M_{2}$ will be $2 v_{0}$ after collision with $M_{1}$ .
Similarly after collision between $M_{2}$ and $M_{3}$ , the velocity of $M_{3}$ will be $2 (2 v_{0})$ . In sequence, the velocity of $M_{4}$ shall be $2 (2 (2 v_{0})) = 8 v_{0}$ after collision with $M_{3} .$

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