# A bucket of water weighing 20 kg is slowly raised from depth of 20 m to ground level by a roap. The mass of rope is 1.2 kg per meter. Find the work done

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

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.

edited Feb 10, 2014 by meena.p