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 the boat move in the water during the process?

• A. 2 m
• B. 1/15 m
• C. 2/15 m
• D. 3/15 m

Answer 1

The correct option is C 2/15 m



Let displacement of the boat 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 should be zero.
$\Delta x_{CM}=\frac{M_b{x}_b+M_v{x}_v+M_m{x}_m}{(M_b+M_v+M_m)}$

$\therefore$ $0=\frac{40x+50(x+2)+60(x-2)}{150}\Rightarrow x=2/15$ m