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 plank is $\frac{M}{3}$, the distance that the man moves relative to the ground is

Answer 1

intially the center of mass is at rest.

therefore the center of mass doesnt move it horizontal direction

it is $\frac{L}{8}$ distance from the end of the man

let'x' be the displacement of plank when the man walks to the other side

then(L-x) be the displacement of the man

let intially the center of mass be at origin$x_i=0$

since the center of mass stationery

$x_i=x_f$

$\frac{L}{8}=\frac{m(L-x)+\frac{m}{3}(\frac{L}{2}-x)}{m+\frac{m}{3}}$

we get $x=\frac{3L}{4}$

the man moved $L-x=\frac{L}{4}distance$