Question

A man of mass 100 kg is standing on a platform of mass 200 kg, which is kept on a smooth ice surface. If the man starts moving on the platform with a speed 30 m/sec relative to the platform, calculate with what velocity relative to the ice the platform will recoil?

• A. 5 m/sec
• B. 10 m/sec
• C. 15 m/sec
• D. 20 m/sec

Hint:

Use the conservation of momentum when two objects move relative to each other.

Answer 1

The Correct Option is B

Step 1: Conservation of Momentum.
By the conservation of momentum, the total momentum before and after the man moves must be equal. Initially, the system is at rest, so: \[ M_{\text{man}} v_{\text{man}} = M_{\text{platform}} v_{\text{platform}} \] where \( M_{\text{man}} = 100 \, \text{kg} \), \( M_{\text{platform}} = 200 \, \text{kg} \), and \( v_{\text{man}} = 30 \, \text{m/s} \).

Step 2: Solve for \( v_{\text{platform}} \).
Using the conservation equation: \[ 100 \times 30 = 200 \times v_{\text{platform}} \] Solving for \( v_{\text{platform}} \): \[ v_{\text{platform}} = \frac{100 \times 30}{200} = 10 \, \text{m/s} \] Thus, the correct answer is (2).