Question

A man of mass $M$ stands at one end of a stationary plank of length $L$, lying on a smooth 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

Answer: (B)

$\frac{L}{4}$

Suppose the distance covered by the man on plank w.r.t plank be $x$, but relative to the ground, distance covered by him is $L-x$.

Hence, comparing the motion of centre of mass,

$\frac{M}{3}x=M(L-x)x=\frac{3}{4}L$

Therefore displacement of man relative to ground $L-x=L-3L/4=\frac{L}{4}$