Question

A girl of mass 30 kg stands at one end of a plank of mass 120 kg and length 4 m. Initially the plank lies at rest on a horizontal frictionless surface. If the girl walks to the other end of the plank, the distance that the girl moves relative to the ground is:

• A. 0.8 m
• B. 1.6 m
• C. 3.2 m
• D. 2 m

Hint:

In problems involving relative motion on frictionless surfaces, use conservation of momentum to find the relative displacements of the objects involved.

Answer 1

The Correct Option is C

Using the principle of conservation of momentum, we can calculate the total distance the girl moves relative to the ground. The velocity of the plank and the girl are related by the equation: \[ m_g \cdot v_g + m_p \cdot v_p = 0 \] Thus, the total displacement of the girl relative to the ground is: \[ d_{\text{total}} = L \cdot \left( 1 + \frac{m_g}{m_p} \right) = 4 \cdot \left( 1 + \frac{30}{120} \right) = 4 \cdot 1.25 = 5 \, \text{m} \]
So, the girl moves 3.2 meters relative to the ground.