Question

Ball A collides with another identical ball B at rest as shown in figure. For what value of coefficient of restitution e the velocity of second ball becomes three times that of A after collision?

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{6}$

Answer 1

Answer: (B)

$\frac{1}{2}$

Answer 2

Let the initial velocities be:

• For ball A: $u$
• For ball B: $0$

After the collision, let the velocities be:

• $v_A$ and $v_B$ respectively with $v_B = 3v_A$.

Step 1: Conservation of Momentum

$$u = v_A + v_B = v_A + 3v_A = 4v_A \quad \Rightarrow \quad v_A = \frac{u}{4}, \quad v_B = \frac{3u}{4}$$

Step 2: Coefficient of Restitution (e)

$$e = \frac{v_B - v_A}{u - 0} = \frac{\frac{3u}{4} - \frac{u}{4}}{u} = \frac{\frac{2u}{4}}{u} = \frac{1}{2}$$