Question

If $u$ is at an angle of ${120}^{\circ }$ with $AB$ and $v$ be the velocity of the second particle, find $\frac{u}{v}$ to the nearest integer.

Answer 1

Initially velocity of centre of mass is (v) of two block system

$v_{com}=\frac{mu+mo}{m+m}=\frac{u}{2}$

at time of u mark angle 120° then velocity of A is let v' and B is v

then $v^{\prime }=\frac{v}{\cos 60°}$

velocity of centre of mass $=\frac{m{v}^{\prime }+mv}{m+m}$

$\frac{u}{2}=\frac{m\frac{v}{\cos 6°}+mv}{2m}\frac{u}{2}=\frac{m\left(3v\right)}{2m}\frac{u}{v}=3$