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Collisions

Question

A steel ball of radius 2 cm is at rest on a frictionless surface. Another ball of radius 4 cm moving at a velocity of 81 cm/sec collides elastically with first ball. After collision the smaller ball moves with speed of (cm/s)

Moderate

Solution

Ratio in radius of steel balls = 1/2
So, ratio in their masses $= \frac{1}{8}$ [As $M \propto V \propto r^{3}$ ]
Let $m_{1} = 8 m$ and $m_{2} = m$
$v_{2} = \frac{2 m_{1} u_{1}}{m_{1} + m_{2}} = \frac{2 \times 8 m \times 81}{8 m + m} = 144 cm / s$

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