Question

A man of mass m hanging with a light rope which is connected with a balloon of mass m. The system is at rest and air at equilibrium. When the man rises

Answer 1

Explanation:

Given A man of mass m hanging with a light rope which is connected with a balloon of mass m. The system is at rest and air at equilibrium. When the man rises  a distance h with respect to balloon. Find distance raised by man and distance descended by balloon.

Let distance raised by man be D

Distance raised by balloon be d

So D + d = h--------------1

So r (centre of mass) = MD – md / M + m = 0

In absence of any force centre of mass does not change.

So MD = md ------------------2

Now MD = m (h – D) (from 1)

MD – mD = mh

D = (m / M – m) h ------------3

Substituting value of D in eqn 1 we get

(m / M – m) h + d = h

So d = h – (m / M – m) h

Or d = Mh – mh – mh / M – m

So d = (M / M – m) h