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Question

The mass of a bucket containing water is M0. The bucket is pulled steadily up from a well of depth d. Due to a hole in the bucket the water is pouring out at a uniform rate and as a result the mass of the bucket with water at the top of the well reduces to M. Then the amount of work done in pulling up the bucket is?

A
(M0M)gd
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B
12(M0M)gd
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C
(M0+M)gd
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D
12(M0+M)gd
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Solution

The correct option is D 12(M0+M)gd
change in mass of bucket per unit length is M0Md
so at any height x from bottom of well mass of bucket is given by M0(M0Md).x
force applied is weight of the bucket at any height x
and work done is froce(F).displacement(ds)
dW=[M0(M0Md).x]g.dx
after integration both side 0toW,0tod
we get
W=12(M0+M)gd
so correct answer is option D.

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