Question

A ball of mass \( 5m \) approaches a stationary ball of mass \( m \) with a horizontal velocity of 2 m/s from left to right. After a perfectly elastic central collision, the horizontal velocity of the heavier ball is 1 m/s from left to right. Which one of the following statements, regarding the velocity (in m/s) of the lighter ball after impact, is TRUE?

• A. Comes to rest
• B. Moves from left to right at 5 m/s
• C. Moves from right to left at 5 m/s
• D. Moves from left to right at 1 m/s

Hint:

In perfectly elastic collisions, both momentum and kinetic energy are conserved. The velocities of the objects after the collision can be determined using these principles.

Answer 1

The Correct Option is B

Step 1: The situation involves a perfectly elastic collision between two balls. We will apply the principles of conservation of momentum and conservation of kinetic energy. 
Step 2: The initial momentum is given by: \[ {Initial momentum} = (5m) \times 2 + m \times 0 = 10m \] After the collision, the heavier ball moves with velocity \( 1 \, {m/s} \), and the lighter ball's final velocity will be \( v \). Using the conservation of momentum: \[ 10m = (5m) \times 1 + m \times v \] Simplifying, we get: \[ 10m = 5m + mv \Rightarrow 5m = mv \Rightarrow v = 5 \, {m/s} \] Step 3: Since the lighter ball moves with a velocity of \( 5 \, {m/s} \) in the same direction as the initial motion of the heavier ball (from left to right), the correct answer is option (B).