$\"\"$

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Weight of the bucket is $\"\"$ kg.

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Height is $\"\"$ m.

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Initially bucket contains $\"\"$ kg of water.

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Weight of the rope is $\"\"$ kg/m.

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At any point of distance $\"\"$ :

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Mass of the rope is $\"\"$ kg.

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36 kg of water finishes draining at 12 m level.

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Therefore, rate of draining is $\"\"$ kg/m.

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Mass of the water is $\"\"$ kg.

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Mass of the bucket is $\"\"$ kg.

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Total mass is $\"\"$ .

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Substitute corresponding values in above expression.

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$\"\"$

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Force $\"\"$ .

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$\"\"$ m/s².

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the work done required to lift the bucket to 12m level from the ground.

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Work done as a Riemann sum is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ J.

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$\"\"$

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Work done required to lift the bucket to 12m level from the ground is $\"\"$ J.