Mr. Verma (50kg) and Mr. Mathur (60kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting frictioin with water how far does the boat move on the water during the process?

Explanation

Let displacement of the boast is `X_(b)=x` towards right
The displacement of Mr. Verma `X_(v)=(x+2)m`
The displacement of Mr. Mathur `X_(m)=(x-2)m`
As no external forces are acting on the system the displacement of the centre of mass of the system shoud be zero.
`/_\x_(CM)=(M_(b)x_(b)+M_(v)x_(v)+M_(M)x_(M))/((M_(b)+M_(v)+M_(m)))`
`:. 0=(40x+50(x+2)+60(x-2))/150impliesx=2/15m`