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Monkey of mass m is holding the end of s...

Monkey of mass m is holding the end of string connected to a balloon of mans M. Length of the string is L and the complete system remains at rest in mid air as shown in figure. Monkey starts to climb to catch the balloon. Calculate distance travelled by balloon by the time monkey reaches the balloon.

Text Solution

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Since not force on the system is zero and initial velocity of the centre of mass is zero hence displacement of the centre of mass remains zero during the motion. When monkey climbs the rope then balloon descends, let distance travelled by the balloon is x in the vertical downward direction. Displacement of monkey with respect to balloon is L in vertical upward direction, hence net displacement of monkey is (L-x) in the upward direction. For zero displacement of centre of mass we can write the following equation:
`m(L-x)=Mx rArr x=(mL)/(m+M)`
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