Question

A 350 kg boat is 12 m long and is floating without motion on still water. A boy of mass 50 kg is at one end. The boy walks to the other end of the boat and stops. The distance in meters moved by the boy with respect to the shore is

• A. 1.7
• B. 1.5
• C. 10.5
• D. 10.3

Answer 1

The correct option is B

1.5

As the boy moved a distance L =12 m , let boat - boy system moves a distance 'x' in opposite direction.

This is because the internal forces cannot shift the centre of mass.

$\therefore$ Distance of boy w.r.to ground = 12 - x

Distance of boat w.r.to ground = (-x)

Displacement of C.O.M w.r.to ground =$△x_{cm}$= 0

$\therefore △x_{cm}=\frac{m_1△x_1+m_2△x_2}{m_1+m_2}\Rightarrow 0=\frac{50(12-x)+350(-x)}{50+350}$

$\Rightarrow 50(12-x)=350(-x)$

$\Rightarrow x=1.5m$