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A block $'A'$ of mass $M$ moving with speed $u$ collides elastically with block $B$ of mass $m$ which is connected to block $C$ of mass $m$ with a spring. When the compression in spring is maximum the velocity of block $C$ with respect to block $A$ is (neglect friction)
Zero
$\frac {M}{M\,+\,m}u$
$\left( {\frac{m}{{M + m}}} \right)u$
$\frac {m}{M}u$
Solution
In first collision between block $A \& B$
$\mathrm{V}_{1}=\left(\frac{\mathrm{M}-\mathrm{m}}{\mathrm{M}+\mathrm{m}}\right) \mathrm{u}+0$
$\mathrm{V}_{2}=\left(\frac{2 \mathrm{M}}{\mathrm{M}+\mathrm{m}}\right) \mathrm{u}+0$
At the time of maximum compression velocities of blocks $B$ and $C$ become equal
$\mathrm{mv}_{2}=\mathrm{mv}+\mathrm{mv}$
$\mathrm{mv}_{2}=2 \mathrm{mv}$
$v=\frac{v_{2}}{2}=\left(\frac{M}{M+m}\right) u$
velocity of $C w . \mathbf{r . t .}$ to $A$
$=\frac{\mathrm{Mu}}{\mathrm{M}+\mathrm{m}}-\left(\frac{\mathrm{M}-\mathrm{m}}{\mathrm{M}+\mathrm{m}}\right) \mathrm{u}=\left(\frac{\mathrm{m}}{\mathrm{M}+\mathrm{m}}\right) \mathrm{u}$
