Question

An inextensible string is passing over a light frictionless pulley. One end of the string is connected to a block of mass $4m$ which is resting on a horizontal surface. To another end, a plate of mass $m$ is attached and is hanging in the air. A particle of mass $m$ strikes from above with vertical velocity $v_0$ and sticks to the plate. Calculate maximum height attained by the block of mass $4m$.

Answer 1

for the whole system

$P_i=P_f$

mv + 0 = (2m + 4m )$v_0$

$v_0=\frac{V}{6}$ m/s ........(1)

from energy conservation

$\frac{1}{2}m{V}^2=6mgx+\frac{1}{2}{v}_0^2$

$\frac{V^2}{2}=6gx+\frac{1}{2}{v}_0^2$ .....(2)

form equation ...(1) s' ..(2) we get

$x=\frac{35V^2}{36\times 12g}$

x is displacement