Question

A rope has a uniform mass density of 0.4 kg/m. The rope is 10 m long and is lowered into a 10 m deep pit. The bottom part of the rope just touches the bottom of the pit. What is the work done to pull the rope out of the well completely? (Assume g = 10m/s^2)

(a) 200 J

(b) 400 J

(c) 2000 J

(d) 4000 J

I had been asked this question during an internship interview.

I want to ask this question from Work Done by a Variable Force in section Work, Energy and Power of Physics – Class 11

Answer 1

Correct option is (a) 200 J

Easiest explanation: Mass density (p) = 0.4 kg/m

Length (l) = 10 m

Force = f(x)

 = m(x)*g

 = 0.4x*g

 = 4x

Displacement (d) = 10 m

Work = \(\int_{0}^{l}\)f(x)dx

 = \(\int_{0}^{10}\)4xdx

 = 200 J.