Question

Mr.Verma (50 kg) and Mr.Mathur (60 kg) 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 friction with water,how far does boat move on the water during the process ?

Answer 1

$m_1=60kg,m_2=40kg,m_3=50kg$

Let A be the origin of the system.

Initially Mr.Verma and Mr.Mathur are at extreme positions of the boat.

Distance of the centre of mass=$\frac{60\times 4+40\times 2+50\times 4}{150}$

=$\frac{280}{150}$=1.87 m from 'A'

when they come to the midpoint of boat,the CM lies at 2 m form 'A'.

Shift in CM=2-1.87=0.13 m right

But as there is no external force in longitudinal direction C.M. would not shift.

So,the boat moves 0.13 m or 13 cm towards right.