Question

A particle of mass $3\text{kg}$ moving with a velocity of $6\hat{i}\text{m/s}$ collides head on with another particle of mass $5\text{kg}$ moving with a velocity of $-2\hat{i}\text{m/s}$. If after the collision, first particle has a speed of $1\text{m/s}$ along the negative $X$ axis, find the coefficient of restitution.

• A. $0.4$
• B. $0.5$
• C. $0.6$
• D. $0.3$

Answer 1

The correct option is A $0.4$

Given,
Mass of first particle, $m_1=3\text{kg}$
Mass of second particle, $m_2=5\text{kg}$
Let $u_1\&u_2$ be the initial velocity of 1st and 2nd particle respectively.
$v_1\&v_2$ be the final velocity of 1st and 2nd particle respectively.

Applying conservation of momentum before and after collision.
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$3\times 6+5\times (-2)=3\times (-1)+5v_2$
${\overrightarrow{v}}_2=\frac{11}{5}\hat{i}=2.2\hat{i}\text{m/s}$

Coefficient of restitution $e=\frac{\text{velocity of separation}}{\text{velocity of approach}}$
$e=\frac{v_2-v_1}{u_1-u_2}=\frac{2.2-(-1)}{6-(-2)}$
$=\frac{3.2}{8}=0.4$
$e=0.4$
The correct option is (a).