Question

The velocities of two steel balls before impact are shown. If after head-on impact the velocity of ball $B$ is observed to be $3ms^{- 1}$ to the right, the coefficient of restitution is

• A. $\frac{7}{18}$
• B. $\frac{6}{7}$
• C. $\frac{5}{18}$
• D. None of these

Answer 1

Answer: (A)

By conservation of linear momentum
$\left(0 . 6\right)\left(4\right)+\left(0 . 4\right)\left(- 2\right)=\left(0 . 6\right)\left(v_{A}\right)+\left(0 . 4\right)\left(3\right)$
$\Rightarrow v_{A}=\frac{2}{3}$
Therefore, $e=\frac{v_{s e p e r a t i o n}}{v_{a p p r o a c h}}=\frac{3 - v_{A}}{4 + 2}=\frac{7}{18}$