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Partially Inelastic Collision

A steel ball ...

Question

A steel ball of radius 2cm is initially at rest on a horizontal frictionless surface. It is struck head on by another steel ball of 4 cm radius travelling with a velocity of $81 c m / s$ . The velocities of two balls after collision are-

72 c m / s

and

56 c m / s

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144 c m / s

and

56 c m / s

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144 c m / s

and

63 c m / s

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63 c m / s

and

72 c m / s

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Solution

The correct option is D $144 c m / s$ and $63 c m / s$
radii give us their masses:8m and m
$u_{1} = 81 c m / s; u_{2} = 0$
$v_{1} = (m_{2} - m_{1}) u_{1} / (m_{2} + m_{1}); v_{2} = (2 m_{1}) u_{1} / (m_{2} + m_{1})$
$v_{1} = 7 m u / 9 m = 9 * 81 / 9 = 63 c m / s; v_{2} = 16 * 81 / 9 = 144 c m / s$

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