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Question

A man of mass m climbs a rope of length L suspended below a balloon of mass M. The balloon is stationary with respect to ground. If the man begins to climb up the rope at a speed vrel (relative to rope). Find velocity of balloon relative to the ground ?

A
V=mMvrel
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B
V=mMvrel
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C
V=mm+Mvrel
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D
V=+mm+Mvrel
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Solution

The correct option is C V=mm+Mvrel
Given that initially the system is at rest,
i.e., VCM=0
So VCM=constant=0
i.e., mv+MVm+M=0
or mv+MV=0[as(m+M)=finite)]
i.e., MV=mv (1)
Furthermore, here it is given that;
vrel=vV (2)
Putting the value of v from Eq. (2) in Eq. (1), we get;
MV=m(vrel+V)
or V=mvrel(m+M) (3)

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