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/m, the work done is _____ (Assume g = 10m/s^2)

(a) 4000 J

(b) 4040 J

(c) 4400 J

(d) 4800 J

I got this question in an internship interview.

This intriguing question originated from Work Done by a Variable Force topic in division Work, Energy and Power of Physics – Class 11

Answer 1

Correct choice is (c) 4400 J

To elaborate: Mass density (p) = 0.2 kg/m

Length (l) = 20 m

Force = f(x)

 = m(x)*g

 = 0.2x*g

 = 2x

Displacement (d) = 20 m

Work = \(\int_{0}^{l}\)f(x)dx+ (20*g*20)

 = \(\int_{0}^{20}\)2xdx + 4000

 = 4400 J.