First slide

The steps in collision

Question

A sphere of mass m moving with a constant velocity v hits another stationary sphere of the same mass m. If e is the coefficient of restitution, then the ratio of velocities of the two spheres, after the collision will be

Moderate

A

1 /e
B

(1 -e) /(1+e)
C

e/(e+1)
D

(e+1)/e

Solution

In case of collision
$\frac{v_{2} - v_{1}}{u_{1} - u_{2}} = e or \frac{v_{2} - v_{1}}{v} = e ∴ v_{2} - v_{1} = ev mv = {mv}_{1} + {mv}_{2} or v = v_{1} + v_{2} Solving eqs . (1) and (2), we get \frac{v_{1}}{v_{2}} = \frac{(1 - e)}{(1 + e)}$

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