A sphere of mass $m $ moving with a constant velocity $u$ hits another stationary sphere of the same mass. If $e$ is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be
A sphere of mass $m $ moving with a constant velocity $u$ hits another stationary sphere of the same mass. If $e$ is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be
$\frac{{1 - e}}{{1 + e}}$
$\frac{{1 + e}}{{1 - e}}$
$\frac{{e + 1}}{{e - 1}}$
$\frac{{e - 1}}{{e + 1}}{t^2}$
A sphere of mass $m $ moving with a constant velocity $u$ hits another stationary sphere of the same mass. If $e$ is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be
Given, $m_{1}=m_{2}=m, u_{1}=u$ and $u_{2}=0$
Let $v_{1}$ and $v_{2}$ be their velocities after collision.
According to momentum conservation, $m u=m\left(v_{1}+v_{2}\right)$
or $u=v_{1}+v_{2} \dots(i)$
By definition $e=\frac{v_{2}-v_{1}}{u-0}$ or $v_{2}-v_{1}=e u \ldots .(i i)$
Solving Eqs. $(i)$ and $(ii),$ we have $v_{1}=\frac{(1-e) u}{2}$
and $v_{2}=\left(\frac{1+e}{2}\right) u$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{1-e}{1+e}$
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