Question

A ball $A$ collides elastically with another identical ball $B$ with velocity $10\text{m/s}$ at an angle of ${30}^{\circ }$ with the line joining their centres $C_1$ and $C_2$. Select the correct alternative(s).

• A. velocity of ball $A$ after collision is $5\text{m/s}$
• B. velocity of ball $B$ after collision is $5\sqrt{3}\text{m/s}$
• C. both the balls move at right angles after collision
• D. kinetic energy will not be conserved here, because collision is not head on

Answer 1

Answer: (A), (B), (C)

The correct options are
A velocity of ball $A$ after collision is $5\text{m/s}$
B velocity of ball $B$ after collision is $5\sqrt{3}\text{m/s}$
C both the balls move at right angles after collision


Velocity component in common tangential direction ($10\sin {30}^{\circ }$) will remain unchanged while velocity components in common normal direction are interchanged in case of an elastic collision.

Since $B$ is initially at rest, it will acquire the velocity component of $A$ in common normal direction ($10\cos {30}^{\circ }$) while $A$ will have only the common tangential component after collision ($10\sin {30}^{\circ }$).

Hence, both $A$ and $B$ move at right angles after collision with $v_A=5\text{m/s}$ and $v_B=5\sqrt{3}\text{m/s}$. Option A, B and C are correct.

Kinetic energy is conserved in an elastic collision, whether it is a head on collision or an oblique collision. i.e option D is incorrect.