A man of mass M hanging with a light rope which is connected with a balloon of mass m. the system is at rest in air. When man rises a distance h with respect to balloon find. The distance raised by man

Options

A. `(mh)/(m+M)`
B. `(Mh)/(m+M)`
C. `(m+M)/(mh)`
D. `(m+M)/(Mh)`

Answer

A

Explanation

Initially `Y_(com)=(ML)/(M+m)`
Since no external force is acting `:.` COM should be at rest
`Deltay_(CM)=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))`
Let baloon descent by a distance x.
`O=(m(x)+M(h-x))/(m+M)`
`ML=(m+M)x`
`x=(Mh)/(m+M)`(Distance descend by balloon )
`L-x=(mh)/(m+M)`(distance raised by man)