Question

A bucket filled with water weighing 20 kg is raised from a well of depth 20 m. If the linear density of the rope is 0.2 kg per meter. the amount of work done is:

• A. 4000J
• B. 4040J
• C. 4400J
• D. 4200J

Answer 1

Answer: (C)

4400J

Weight of bucket + Rope of length x$=m=20+0.2x$

Work done in raising the rope+bucket by depth $dx=dW=mg\left(dx\right)$

Integrating both sides from $x=0m$ to $x=20m$

$\Rightarrow W={\int }_0^{20}(20+0.2x)\left(10\right)\left(dx\right)$

$\Rightarrow W=4000+400=4400J$

Hence, correct answer is option $C$