Question

A 500 kg boat is 9 m long and is floating without motion on still water. A man of mass 100 kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is :

• A. 1.5 m in the direction of displacement of the man
• B. 0.75 m in the direction of displacement of the man
• C. 1.5 m in the direction opposite to the displacement of the man
• D. 0.75 m in the direction opposite to the displacement of the man

Answer 1

Answer: (C)

1.5 m in the direction opposite to the displacement of the man

As there is no external force, the center of mass of the boat+man system remains at the same position. The displacement of boat would be in opposite direction to that of the man, to maintain same position for CoM.

Let the displacement of boat be $x$, in direction opposite to the displacement of man.

So net displacement of man is $(9-x)$

So, $M_{man}\times (9-x)=M_{boat}\times x$

$⟹100(9-x)=500x⟹x=900/600=1.5m$

Option C is correct.