A balloon of mass $M$ with a light rope and monkey of mass $m$ are at rest in mid air. If the monkey climbs up the rope and reaches the top of the rope, the distance by which the balloon descends will be(Total length of the rope is $L$ )
$\frac{{mL}}{{{{(m + M)}^2}}}$
$\frac{{mL}}{{{{m + M}}}}$
$\frac{{(m + M)L}}{m}$
$\frac{{(M + m)}}{{mL}}$
What is the moment of inhertia of a solid sphere of radius $R$ and density $\rho $ about its diameter ?
Four particles of masses $m_1 = 2m,\, m_2 = 4m,\, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square?
Three masses of $2\,kg$, $4\, kg$ and $4\, kg$ are placed at the three points $(1, 0, 0)$ $(1, 1, 0)$ and $(0, 1, 0)$ respectively. The position vector of its center of mass is
$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strike the rod with a velocity $v_0$ at point $C$ a distance $x$ from the centre $O$. The particle comes to rest after collision. The value of $x$, so that point $A$ of the rod remains stationary just after collision, is :