Question

A wooden plank of mass $20\text{kg}$ 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. The length of the plank is $10\text{m}$. Find the displacement of the plank over the floor, when the man reaches the other end of the plank.

• A. $7.5\text{m}$
• B. $8.5\text{m}$
• C. $9.5\text{m}$
• D. $6.5\text{m}$

Answer 1

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

For the (man $+$ plank) system, net force on the system in the horizontal direction is zero.

Also, the centre of mass of the system is at rest.

Therefore, the displacement of its centre of mass in horizontal direction is zero.

Let $x$ be the displacement of the plank.

Here, $x_{COM}=\text{same},\because F_{net}=0$,

So we can apply formula directly

$x=\frac{mL}{m+M}$

Here,
$M=20\text{kg};m=60\text{kg};L=10\text{m}$

$x=\frac{60\times 10}{60+20}$

$\therefore x=7.5\text{m}$

Hence, option $\left(A\right)$ is correct.