Question

A person draws water from a 5 m deep well in a bucket of mass 2kg of capacity 8 litres by a rope of mass 1kg. What is the total work done by the person? (Assume \[g=10m{{s}^{-2}}\])
A) 550J
B) 525J
C) 125J
D) 500J

Answer 1

Hint: We need to understand the relation between the mass of the bucket used, the mass of the rope used and the capacity of the bucket with the expenditure of energy on pulling a bucket full of water from the bottom of a well to solve this problem.

Complete answer:
We are given a system in which a bucket of water of specific volume is pulled up from a well using a rope. We are given the volume of water which is lifted up from the well. We already know the density of the water so we can find the mass of water that is lifted from the well.

We know that the mass of the rope is 1 kg. If the length of the rope is 5m, assuming the rope is uniformly thick, then the center of mass of the rope is at 2.5 m. Now, we can find the work done against the gravitational force by the bucket of water and the rope from these data.
The mass of water in the bucket is given by –
\[\begin{align}
  & \text{Density = }\dfrac{\text{Mass}}{\text{Volume}} \\
 & \Rightarrow M=\rho V \\
 & \Rightarrow M=1kg{{m}^{-3}}\times 8l \\
 & \therefore M=8kg \\
\end{align}\]
The work done by the system is given by –
\[\begin{align}
  & \text{Total work done = Work done by bucket and water + Work done by the rope} \\
 & \Rightarrow W={{W}_{w}}+{{W}_{r}} \\
 & \Rightarrow W=({{m}_{w}}+{{m}_{b}})gh+{{m}_{r}}g\dfrac{h}{2} \\
 & \Rightarrow W=(8+2)10(5)+(1)(10)(2.5) \\
 & \therefore W=525J \\
\end{align}\]
The total work done by the bucket containing the water and the rope in lifting the water from the well is 525J.

The correct answer is option B.

Note:
The work done in lifting an object from a depth against gravitational force is completely dependent on the mass of the object which is pulled up. The rope directly pulling the bucket from the well is different from the situation in which a pulley is used.