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Velocity of Separation and Approach

Particle 1 co...

Question

Particle 1 collides a stationary particle 2 head on elastically. Find their mass ratio if after collision they move in opposite direction with equals velocities.

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Solution

The correct option is C 1/3
$\frac{v_{1}}{v_{2}} = \frac{(m_{1} - m_{2}) u_{1} + 2 m_{2} u_{2}}{(m_{2} - m_{1}) u_{1} + 2 m_{1} u_{1}}$

or $- 1 = \frac{(m_{1} - m_{2}) u}{2 m_{1} u}$ or $\frac{m_{1}}{m_{2}} = \frac{1}{3}$ .

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