Question

A wooden plank of mass $20\text{kg}$ and length $10\text{m}$ is resting on a smooth horizontal floor. A man of mass $60\text{kg}$ starts moving from one end of the plank to the other end. Find the magnitude of displacement of the plank over the floor when the man reaches the other end of the plank.

• A. $7.5\text{m}$
• B. $5\text{m}$
• C. $12.5\text{m}$
• D. $2.5\text{m}$

Answer 1

The correct option is A $7.5\text{m}$

Here, the system is (man + plank). Net force on this system in horizontal direction is zero and initially the centre of mass of the system is at rest. Therefore, the centre of mass does not move in horizontal direction.

Given:
Mass of man $m_m=60\text{kg}$
Mass of plank $m_p=20\text{kg}$
Let $\Delta x_p=x\text{m}$ be the distance the plank has moved. Assuming the origin, i.e. $\text{x}=0$ at the position shown in figure.
$\Rightarrow$Distance travelled by man$\Delta x_m=(10-\text{x})\text{m}$

As we said, the centre of mass will not move in horizontal direction. $\therefore \Delta x_{com}=0$
$\Rightarrow m_p\Delta x_p=m_m\Delta x_m$
$\Rightarrow 20\times x=60\times (10-x)$
$x=\frac{30}{4}\text{m}=7.5\text{m}$