Question

The mass of a bucket full of water is 15kg it is being pulled up from 15m deep well. Due to hole in the bucket 6kg water flows out of the bucket . The work done in drawing the bucket out of the well is

Answer 1

If we consider the water is flown out of the bucket at a constant rate with depth ,then consider the work done in lifting the bucket though height dh and integrate it to full depth.
Answer =1800 J

Answer 2

mass varies from deep of well to 15 m in height .
let ¢ is mass per unit height . 
so, 
dm  = ¢dx 
       =  6/15dx 

M =  m-dm

now,

workdone = change in potential energy 
= F× x
= ( m -dm)g ×  x
= mgx -dm×gx 
= 15 × 10 × 15 -6/15 gx.dx
=2250 - 6/15 x10x 225/2 
=2250 -  3 x 15x 10
= 2250 - 450
= 1800 Joule
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