A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If…

Solution

$\mathrm{mv}+0={\mathrm{mv}}_1+{\mathrm{mv}}_2$

${\mathrm{v}}_1+{\mathrm{v}}_2=\mathrm{v}$ ....(i)

$\mathrm{e}=\frac{{\mathrm{v}}_2-{\mathrm{v}}_1}{\mathrm{v}-0}$

$\mathrm{ev}={\mathrm{v}}_2-{\mathrm{v}}_1$ ..(ii)

Add equation (i) & equation (ii)

$\mathrm{ev}+\mathrm{v}=2{\mathrm{v}}_2$

${\mathrm{v}}_2=\frac{\mathrm{v}(\mathrm{e}+1)}{2}$

$\frac{{\mathrm{v}}_2}{\mathrm{v}}=\frac{\mathrm{e}+1}{2}=0.75$
 

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