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Question

The mass of bucket full of water is 15 kg . It is being pulled up from a 15 m deep well. Due to a hole in the bucket 6 kg water flows out of the bucket at a uniform rate. The work done in drawing the bucket out of the well will be (g=10m/s2)−

A
900 J
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B
1500 J
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C
1800 J
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D
2100 J
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Solution

The correct option is C 1800 J
Step 1: Water in bucket at height x
Mass of bucket full of water =15 kg
Water goes out of bucket =6 kg
Out flow of water per meter of pull =6kg15m
=0.4 kg/m
Water in the bucket at height x from bottom (m) =(150.4x)kg
m=(150.4x)

Step 2: Work done
Work done in pulling the bucket by small distance (dx)
dW=mg dx
dW=(150.4x)g dx

Step 3: Integration
For total work done integrate from x=0 to x=15 m
W=150(150.4x)g x

W=g[15x0.4x22]150

W=10(22545)
W=1800 J

Option C is correct.

Alternate Solution:

Here work done by gravity is linear function of height (x)
So we can find average water leak in this case-
Average weight leak =3 g Kg - wt
So remaining =(153) g=12 g Kg - wt

Work done =F×d =12 g×15 =120×15

W=1800 J

Note:
This method is only applicable for the linear function of height.
If work done by gravity is a non-linear function of x then, don't use this approach
e.g. If W=mgx3
Here we can not apply this method

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