Question

Two balls of masses $2\text{kg}$ and $4\text{kg}$ are moving towards each other with speeds $6\text{m/s}$ and $4\text{m/s}$ respectively, on a frictionless surface. If the coefficient of restitution is $0.5$, the relative velocity of seperation between the two balls is

• A. $1\text{m/s}$
• B. $2\text{m/s}$
• C. $5\text{m/s}$
• D. $-1\text{m/s}$

Answer 1

The correct option is C $5\text{m/s}$

Given,
Mass of ball 1 $\left(m_1\right)=2\text{kg}$
Mass of ball 2 $\left(m_2\right)=4\text{kg}$
Velocity of ball 1 $\left(u_1\right)=6\text{m/s}$
Velocity of ball 2 $\left(u_2\right)=-4\text{m/s}$ (opposite)
Coefficient of restitution $\left(e\right)=0.5$

Since coefficient of restitution $e=\frac{\text{velcocity of separation}}{\text{velocity of approach}}=\frac{v_2-v_1}{u_1-u_2}$
$\Rightarrow v_2-v_1=e(u_1-u_2)$
$\Rightarrow v_2-v_1=0.5(6-(-4\left)\right)$
$=5\text{m/s}$