Question

A ball collides directly with another ball at rest and is itself brought to rest by the impact. If one fourth of initial kinetic energy is destroyed in the collision, the coefficient of restitution of the collision is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{3}{4}$
• D. $\frac{1}{3}$

Answer 1

The correct option is C

$\frac{3}{4}$

$m_1{u}_1=m_2{v}_{2}ande=\frac{V_2-V_1}{u_1-u_2}=\frac{V_2}{u_1}\Rightarrow V_2=e{u}_1{m}_1{u}_1=m_{2}e{u}_1\Rightarrow m_1=e{m}_2$

Loss of kinetic energy.
$=\frac{1}{2}\frac{m_1{m}_2}{m_1+m_2}(u_1-0{)}^2(1-e^2)=\frac{1}{4}\times \frac{1}{2}{m}_1{u}_1^2$

$\frac{m_2}{m_1+m_2}(1-e^2)=\frac{1}{4}\frac{m_2}{e{m}_2+m_2}(1-e^2)=\frac{1}{4}\Rightarrow 1-e=\frac{1}{4}e=\frac{3}{4}$