A big ball of mass M, moving with velocity

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A big ball of mass $M$, moving with velocity $u$ strikes a small ball of mass $m$, which is at rest. Finally small ball obtains velocity $u$ and big ball $v$. Then what is the value of $v$

A

$\frac{{M - m}}{{M }}u$

B

$\frac{m}{{M + m}}u$

C

$\frac{{2m}}{{M + m}}u$

D

$\frac{M}{{M + m}}u$

A big ball of mass $M$, moving with velocity $u$ strikes a small ball of mass $m$, which is at rest. Finally small ball obtains velocity $u$ and big ball $v$. Then what is the value of $v$

By momentom conservation,

$Mu = Mv + mu$

$v =\frac{( M - m ) u }{ M }$