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 other end of the plank. If the mass of the plank is $\frac{ M }{3}$, then the distance that the man moves relative to ground is :

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

Answer 1

Answer: (B)

Le the distance moved by plank is $x$
$m _{1} \Delta x _{1}+ m _{2} \Delta x _{2}=0$
$M ( L - x )+\frac{ M }{3}(- x )=0 $
$\Rightarrow x =\frac{3 L }{4}$
$\therefore $ distance moved by person w.r.t. to ground
$= L - x =\frac{ L }{4}$