Question

A ball P in motion collides with another ball Q of same mass at rest. If the coefficient of restitution between the two balls is 0.2, then the ratio of the velocities of the two balls P and Q after collision is:

• A. 1:3
• B. 2:3
• C. 1:1
• D. 3:4

Hint:

For 1D collision always use momentum + restitution together.

Answer 1

The Correct Option is A

Step 1: Let initial velocity of P be $u$, Q is at rest.
Step 2: Conservation of momentum: \[ mu = mv_P + mv_Q \Rightarrow u = v_P + v_Q \quad (1) \]
Step 3: Coefficient of restitution: \[ e = \frac{v_Q - v_P}{u - 0} = 0.2 \] \[ v_Q - v_P = 0.2u \quad (2) \]
Step 4: Solve (1) and (2): From (1): $v_Q = u - v_P$ Substitute: \[ (u - v_P) - v_P = 0.2u \] \[ u - 2v_P = 0.2u \]
Step 5: \[ 0.8u = 2v_P \Rightarrow v_P = 0.4u \]
Step 6: \[ v_Q = 0.6u \]
Step 7: Ratio: \[ v_P : v_Q = 0.4 : 0.6 = 2:3 \]