Question

A man of mass $m$ is standing in a lift of the same mass m which is balanced on a pulley by a block of mass $2m$. If the man jumps suddenly with a velocity $V_0$ upwards with respect to ground, then the speed of the man relative to lift just after he jumps would be

• A. $v_0$
• B. $\frac{v_0}{3}$
• C. $\frac{2v_0}{3}$
• D. $\frac{4v_0}{3}$

Answer 1

The correct option is D $\frac{4v_0}{3}$

Consider (man + lift + block 2m) as system
For this system momentum is conserved along the string.
Let $v$ be the speed of lift downwards
$P_i=P_f$
$0=m{v}_o-(m+2m)v$
$v=\frac{v_o}{3}\Rightarrow {\overrightarrow{V}}_{man,lift}={\overrightarrow{v}}_{man}-{\overrightarrow{v}}_{lift}\Rightarrow {\overrightarrow{v}}_{m,l}=v_o-\left(\frac{-v_0}{3}\right)=\frac{4v_o}{3}$