Two men $A$ and $B$ are standing on the opposite edge of a $6 \mathrm{m}$ long platform which is further kept on a smooth floor. They start moving towards each other and finally meet at the midpoint of the platform. Find the displacement of the platform if the mass of $A$, $B$ and $C$ platform are $40 \mathrm{kg}$, $60 \mathrm{kg}$ and $50 \mathrm{kg}$, respectively.

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

In a process, a neutron which is initially at rest decays into a proton, an electron and an antineutrino. The ejected electron has a momentum of $p_1=2.4\times {10}^{–26} \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$ and the antineutrino has $p_2=7.0\times {10}^{–27} \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$. Find the recoil speed of the proton if the electron and the antineutrino are ejected

$\left(\mathrm{a}\right)$ along the same direction.

$\left(\mathrm{b}\right)$ in mutually perpendicular directions. (Mass of the proton $m_p=1.67\times {10}^{–27} \mathrm{kg}$.)