A sphere of mass m moving with a constant ve | vedclass

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Question

(a) 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 conservatio

Vedclass · Accepted Answer

$\frac{{1 - e}}{{1 + e}}$

Vedclass · Answer

(a) 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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