Question

A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{M}{3}$, the distance that the man moves relative to the ground is

• A. $\frac{3L}{4}$
• B. $\frac{L}{4}$
• C. $\frac{4L}{5}$
• D. $\frac{L}{3}$

Answer 1

The correct option is B $\frac{L}{4}$

Let plank moves $x$ distance in oppsoite direction. Then, displacement of man relative to ground will be, ($L-x$).
Applying
$m_m{x}_m=m_p{x}_p$
or $M(L-x)=\frac{M}{3}x$
Solving this equation we get, $x=\frac{3L}{4}$
$\therefore$ Displacement of man relative to ground = $L-\frac{3L}{4}=\frac{L}{4}$