\[(a)\;3920\;J \quad (b)\;2352\;J \quad (c)\;6722\;J \quad (d)\;6272\;J\]

Weight of bucket alone $=20 \times 9.8 \;N$

work done to overcome weight of bucket in lifting to 20 m is

$\quad=20 \times 9.8 \times 20$

$\quad=3920\; J$

Mass of rope 20 m long

$\quad=20 \times 1.2$

$\quad= 24\; kg$

The weight of rope

$\quad=24 \times 9.8$

$\quad=235.2\;N$

The weight acts at center of gravity and so the C.G of rope is lifted up by 10 m only

Therefore Work done to raise rope

$\quad=235.2 \times 10$

$\quad=2352 \;J$

Total work done

$\quad= 3920+2352$

$\quad=6272\;J$

hence d is the correct answer.

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