Question

A sphere $A$ moving with speed $u$ and rotating with an angular velocity $\omega$ makes a head-on elastic collision with an identical stationary sphere $B$. There is no friction between the surfaces of $A$ and $B$. Choose the correct alternative(s). Discard gravity.

• A. $A$ will stop moving but continue to rotate with an angular velocity $\omega$
• B. $A$ will come to rest and stop rotating
• C. $B$ will move with speed $u$ without rotating
• D. $B$ will move with speed $u$ and rotate with an angular velocity $\omega$.

Answer 1

Answer: (A), (C)

$A$ will stop moving but continue to rotate with an angular velocity $\omega$
$B$ will move with speed $u$ without rotating

Let $m$ be the mass of sphere and $v_1$ and $v_2$ be the velocities of the spheres A and B respectively after the collision.

Applying conservation of linear momentum: $P_i=P_f$

$mu+0=m{v}_1+m{v}_2⟹v_1+v_2=u$ ........(1)

Also $\frac{v_2-v_1}{u-0}=-1⟹v_1-v_2=-u$

On solving we get, $v_1=0$ and $v_2=u$

Thus A will stop and B will move with $u$

Also as there is no friction between the A and B, thus there will be no torque. Hence angular velocities of the respective spheres must remains the same as it was initially.

So, A will continue to rotate with $w$ whereas B will not rotate.