Question

In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor throws a stone of mass $m$ downwards with a speed $u$. When the stone reaches the floor, distance of the man above the floor will be :

• A. $h$
• B. $2h$
• C. $h-\frac{2mh}{M}$
• D. $\frac{mh}{M}+h$

Answer 1

The correct option is D $\frac{mh}{M}+h$

In gravity free space, no external force acts on the system, hence the total momentum is conserved.

Hence, $mu=M{V}_{man}$

$⟹V_{man}=\frac{mu}{M}$

Time taken by stone to reach floor, $t=\frac{h}{u}$

Hence the distance traveled by man upwards $=V_{man}t$ $=\frac{mu}{M}\times \frac{h}{u}$ $=\frac{mh}{M}$

Hence, the total distance between man and floor $=\frac{mh}{M}+h$