Question

A particle loses 25% of its energy during collision with another identical particle at rest the coefficient of restitution will be :

• A. 0.25
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. 0.5

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}$

Given : $m_1=m_2=m$ $u_1=u$ $u_2=0$

Let the particle is moving with speed $u$ before collision.

Initial K.E of the system $K.E_i=\frac{1}{2}m{u}^2$

$\therefore$ Loss in Kinetic energy $\Delta K.E=\frac{1}{4}K.E_i=\frac{1}{8}m{u}^2$

Loss in Kinetic energy $\Delta K.E=\frac{1}{2}\frac{m_1{m}_2}{m_1+m_2}(u_1-u_2{)}^2(1-e^2)$

$\frac{1}{8}m{u}^2=\frac{1}{2}\frac{m\times m}{m+m}{u}^2(1-e^2)$

$\frac{1}{2}=1-e^2$ $⟹e=\frac{1}{\sqrt{2}}$