A particle of mass m collides with a heavy ma | vedclass

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Question

$\mathrm{mu}_{1}+0=\mathrm{m}\left(-\mathrm{v}_{1}\right)+\mathrm{mv}_{2}$               $\ldots(i)$

For $m

Vedclass · Accepted Answer

$5$

Vedclass · Answer

$\mathrm{mu}_{1}+0=\mathrm{m}\left(-\mathrm{v}_{1}\right)+\mathrm{mv}_{2}$               $\ldots(i)$

For $m$ mass.

$\mathrm{k}^{\prime}=\frac{4}{9} \mathrm{k}$

$\Rightarrow \mathrm{v}_{1}=\frac{2}{3} \mathrm{u}_{1}$          $...(ii)$

For heavy body

$\frac{1}{2} \mathrm{Mv}_{2}^{2}=\frac{5}{9} \frac{1}{2} \mathrm{mu}_{1}^{2}$

from eq $( ii )$

$\mathrm{Mv}_{2}=\sqrt{\frac{5}{9} \mathrm{mM}} \mathrm{u}_{1}$           $...(iii)$

From eq. $(i),$ $( ii )$ and $(iii)$

$\mathrm{m}\left(\mathrm{u}_{1}+\mathrm{v}_{1}\right)=\sqrt{\frac{5}{9} \mathrm{mM}} \mathrm{u}_{1}$

$\mathrm{m} \frac{5}{3} \mathrm{u}_{1}=\frac{\sqrt{5 \mathrm{mM}}}{3} \mathrm{u}_{1}$

$\mathrm{M}=5 \mathrm{m}$

A particle of mass $m$ collides with a heavy mass (at rest) elastically and after collision returns with $4/9$ of it's initial kinetic energy. The mass of heavy object is ............... $\mathrm{m}$

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