A man of mass m stands at one end of a plank of length l which lies at rest on a frictionless horizontal surface. The man walks to the other end of the plank. If the mass of the plank is m/3 the distance that the man moves relative to the ground will be _________

(a)

(b)

(c)

(d)

Initially the centre of mass is at rest.

There is no external force acting on the system so linear momentum is conserved.

Hence speed of centre of mass given as:

Where,

Mass of particle

Mass of particle

Initial speed man

Initial speed plank

Final speed of man

Final speed of plank

Given, initially both the particles at rest, so,

We Know, speed of centre of mass at any instant is

Using,

In expression of V_CM, we get,

Hence centre of mass remains at rest.

So we first calculate the position of centre of mass at t=0

Let walking to end man travels a distance a.

CM of Plank shifts a distance (L-a) in the opposite direction.

Since, CM of system remains at same position.

Distance that the man moves relative to the ground is