A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:

(\frac{1 - e}{1 + e})

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(\frac{1 + e}{1 - e})

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(\frac{e + 1}{e - 1})

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(\frac{e - 1}{e + 1})

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Solution

The correct option is A $(\frac{1 - e}{1 + e})$
$e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} = \frac{v_{2} - v_{1}}{u}$
$e u = v_{2} - v_{1}$
For head on elastic collision: $u = v_{1} + v_{2}$
On solving we get:
$v_{1} = (1 - e) \frac{u}{2}, v_{2} = (1 + e) \frac{u}{2}$
$\frac{v_{1}}{v_{2}} = \frac{1 - e}{1 + e}$

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A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:

The correct option is A (1−e1+e)e=v2−v1u1−u2=v2−v1ueu=v2−v1 For head on elastic collision: u=v1+v2On solving we get: v1=(1−e)u2,v2=(1+e)u2v1v2=1−e1+e