A body of mass 50 gm collides elastically with another body of mass 30 gm at rest. Then the percentage loss of the velocity of the colliding body during collision is

$\frac{{\text{u}}_{\text{1}}-{\text{v}}_{\text{1}}}{{\text{u}}_{\text{1}}}\times 100=?\Rightarrow \left(1\right)$

${\text{v}}_{\text{1}}=\frac{{\text{m}}_{\text{1}}-{\text{m}}_{\text{2}}}{{\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}}{\text{u}}_{\text{1}}+\frac{{\text{2m}}_{\text{2}}{\text{u}}_{\text{2}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

${\text{v}}_{\text{1}}=\frac{{\text{m}}_{\text{1}}-{\text{m}}_{\text{2}}}{{\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}}{\text{u}}_{\text{1}}+0$

$=\frac{50-30}{50+30}{\text{u}}_{\text{1}}$

${\text{v}}_{\text{1}}=\frac{20}{80}{\text{u}}_{\text{1}}\Rightarrow \frac{{\text{u}}_{\text{1}}}{\text{4}}\Rightarrow \left(2\right)$

Substitute (2) in (1)

$\frac{{\text{u}}_{\text{1}}-\frac{{\text{u}}_1}{4}}{{\text{u}}_{\text{1}}}\times 100$

$\frac{3}{4}\times 100\to 75\%$