Question

Ball $A$ of mass $50gm$ and speed $10m/s$ collides with other ball $B$ of mass $10gm$ and speed $15m/s$ travelling in opposite direction with each other. Determine the final speed of ball $B$, if the coefficient of restitution is $\frac{2}{5}$.

• A. $\frac{40}{3}m/s$
• B. $\frac{75}{3}m/s$
• C. $\frac{91}{8}m/s$
• D. $\frac{85}{6}m/s$

Answer 1

Answer: (D)

Given, $m_A=50gm,u_A=10m/s,m_B=10gm$
$u_B=-15m/s$ and coefficient of restitution, $e=\frac{2}{5}$
The collision of ball $A$ and $B$ is shown as below,

Velocity of second ball $B$ is given by the relation,
$v_B=\frac{m_A(1+e)}{m_A+m_B}{u}_A+\frac{m_B-e{m}_A}{m_A+m_B}{u}_B$
Putting the given values in above relation, we get
$\Rightarrow v_B=\frac{50\left(1+\frac{2}{5}\right)}{50+10}\times 10+\frac{10-50\times \frac{2}{5}}{50+10}(-15)$
$\Rightarrow v_B=\frac{50\times 7\times 10}{60\times 5}+\frac{10\times 15}{60}$
$\Rightarrow v_B=\frac{70}{6}+\frac{15}{6}=\frac{85}{6}m/s$