First slide

Motion of centre of mass

Question

If fig four identical spheres of equal mass m are

suspended by wires of equal length /, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and
all collisions are elastic, the velocity of sphere 4 iust after collision is

Moderate

A

$\sqrt{(2 gl)}$
B

$\sqrt{(3 gl)}$
C

$\sqrt{(gl)}$
D

$\sqrt{(gl)} / 2$

Solution

. When the sphere 1 is released from horizontal position, then potential energy at height / = kinetic energy at bottom
$or mgl = \frac{1}{2} {mv}^{2} v = \sqrt{(2 gl)}$
$Now, the velocity of sphere 1 is transforred to sphere 2 felastic collision), then from 2 to sphere 3 and finally from sphere 3 to sphere 4 Therefore, the sphere 4 attains " velocity \sqrt{(2 gl)}$

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