Water is dragged from a well of hepth 30 m using bucket of weight 50kg with water If the weight of the rope is 0.4 kg per metre, the amount of work done is ;

Given

Depth of well $=30 \mathrm{~m}$

weight of bucket + water $=50 \mathrm{~kg}$

mass per unit length of rope $=0.4 \mathrm{~kg}$

mass of length $x+$ mass of bucket + weight $=$ $(0.4 x+50) \mathrm{kg}$

weight of rope $+($ bucket + water $)=(0.4 x+50) g$ work done in lifting the rope $t$ bucket + water by $d x=$

$(0.4 x+50) g d x$

Total work done in lifting from

$\begin{aligned} 0 \text { to } 30 m & =\int_{0}^{30}(0.4 x+50) g d x \\ & =0.4 g \frac{x^{2}}{2}+\left.50 x g\right|_{0} ^{30} \\ & =0.2 g \times 30 \times 30+50 \times 30 \times g \\ & =0.2 \times 900 \times 9.8+1500 \times 9.8 \\ & =1764+14700 \\ & =16464 \text { J0ule } \end{aligned}$

Hence, the amount of work done is 16464 J