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  4. A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be

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Q. A man of $50\, kg$ mass is standing in a gravity free space at a height of $10 \,m$ above the floor. He throws a stone of $0.5 \,kg$ mass downwards with a speed $2 \,m/s$. When the stone reaches the floor, the distance of the man above the floor will be

AIPMTAIPMT 2010Gravitation

Solution:

Since the man is in gravity free space, force on man $ +$ stone system is zero.
Therefore centre of mass of the system remains at rest.
Let the man goes $x \,m$ above when the stone reaches the floor, then
$ M_{\text{man}} \times x = M_ {\text{stone}} \times 10 $
$ x= \frac{ 0.5}{50} \times 10 $
$ x= 0.1 m $
Therefore final height of man above floor $= 10 + x$
$= 10 + 0.1 = 10.1 \,m$

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