Question

A man of mass 30kg is standing at one end of stationary floating plank of mass 40kg.the length of the plank is 7m if man moves to other end of plank then the distance by which plank moves is

Answer 1

1.75 m is the right answer

Answer 2

Concept

Centre of mass is an imaginary point where the full mass of an object is also concentrated.

Given

We are given a mass of the person is $30kg$  which is standing and also the mass of stationary floating plank is $40kg$ and also the length of plank is $7m.$

Find

We have to seek out the space by which plank moves.

Solution

Mass of man $=30kg$

Mass of plank $=40kg$

Let man is standing at the starting of plank, at $x=0$ end of plank, $x=7$ Center of Mass of man is at $x=0$

Center of Mass of plank is at $x=\frac{7}{2}=3.5$

Center of Mass of system$=\frac{30\times 0+40\times 3.5}{30+40}=2m$

Consider man walking to one end to other and complet a distance $s$.

Center of mass of man is at $x=s$

Hence, the Center of mass of plank will shift to $(7-s)$ towards left,

Center of mass of plank is at $=[3.5-(7-s)]=(s-3.5)$

Center of mass of system does not change its position as there is no external force.

$\begin{aligned}2&=\frac{30\times s+40\times(s-3.5)}{30+40}\\ 140&=30s+40s-140\\ s&=4\end{aligned}$

Hence, the distance by which plank will move is $4m$.

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