Question

Ball $A$ of mass $50\, gm$ and speed $10\, m / s$ collides with other ball $B$ of mass $10 \,gm$ and speed $15 \,m / s$ 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, $m_{A}=50\, gm , u_{A}=10 \,m / s , m_{B}=10\, gm$
$u_{B}=-15 \,m / s$ 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,
$v_{B}=\frac{m_{A}( 1 +e)}{m_{A}+m_{B}} u_{A}+\frac{m_{B}-em_{A}}{m_{A}+m_{B}} u_{B}$
Putting the given values in above relation, we get
$\Rightarrow \,v_{B}=\frac{50\left(1+\frac{2}{5}\right)}{50+10} \times 10+\frac{10-50 \times \frac{2}{5}}{50+10}(-15)$
$\Rightarrow \,v_{B}=\frac{50 \times 7 \times 10}{60 \times 5}+\frac{10 \times 15}{60}$
$\Rightarrow \, v_{B}=\frac{70}{6}+\frac{15}{6}=\frac{85}{6} \,m / s$