Question

Two billiard balls are in contact on a table. A third identical ball strikes them symmetrically with speed $u$ and comes to rest after impact.

• A. Speed of other balls become $\frac{u}{2}$ after impact
• B. Speed of other balls become $\frac{u}{\sqrt{3}}$ after impact
• C. The coefficient of restitution is $\frac{1}{2}$
• D. The coefficient of restitution is $\frac{2}{3}$

Answer 1

Answer: (B), (D)

The correct options are
B Speed of other balls become $\frac{u}{\sqrt{3}}$ after impact
D The coefficient of restitution is $\frac{2}{3}$


Using conservation of momentum along horizontal direction
$m{V}_1\cos {60}^{\circ }=m{V}_1\cos {60}^{\circ }$
$V_1=V_2=V$
Using conservation of momentum along vertical direction
$2mV\sin {60}^{\circ }=mu$
$V=\frac{u}{\sqrt{3}}$

Co-efficient of restitution along common normal
$e=\frac{V-0}{u\cos {30}^{\circ }}=\frac{\frac{u}{\sqrt{3}}}{\frac{u\sqrt{3}}{2}}=\frac{2}{3}$