Question

A boy of mass 50kg is standing on a frictionless surface. He throws a ball of mass 2kg away from him with a speed of 10m/s. Find the final speed of the centre of mass.

• A. 0m/s
• B. 20m/s
• C. 10m/s
• D. 0.4m/s

Hint:

For systems with no external forces, the center of mass moves with a constant velocity, and the total momentum is conserved.

Answer 1

The Correct Option is A

Step 1: Apply conservation of momentum.
Since there are no external forces, the total momentum of the system must remain zero.
Initially, both the boy and the ball are at rest, so the initial momentum is zero.

Step 2: Use the momentum formula.
The momentum before and after the throw must satisfy: \[ m_{\text{boy}} \times v_{\text{boy}} + m_{\text{ball}} \times v_{\text{ball}} = 0 \] Substitute the known values: \[ 50 \times v_{\text{boy}} + 2 \times 10 = 0 \] Solving for \( v_{\text{boy}} \), we get: \[ v_{\text{boy}} = - \frac{2 \times 10}{50} = -0.4 \, \text{m/s} \] Since the center of mass speed is the average velocity of the system, it will be zero because the boy's movement cancels the ball's momentum.