Question

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

Answer 1

${\text{Initially Y}}_{com}=\frac{ML}{M+m}$

Since no external force is acting

$\therefore \text{COM should be at rest}$

${\Delta }_{YCM}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

$\text{Let balloon descent by a distance x.}$

$O=\frac{m\left(x\right)+M(h-x)}{m+M}$

$ML=(m+m)x$

$x=\frac{Mh}{m+M}\left(\text{Distance descend by balloon}\right)$

$L-x=\frac{mh}{m+M}\left(\text{Distance raised by man}\right)$