Given Information: The weight of the chain is 25 lb and the length of the chain is 10 ft .

Concept Used: The work done by a force F in moving a particle from x1 to x2 is given by

  W=∫x1x2F(x)dx

Calculation:The weight per unit length of the chain is weightlength=2510=2.5

An infinitesimally small element of length dx having a weight 2.5 ×dx at a distance x below the mid-point of the rope reaches a position which is at a distance x above the midpoint of the rope. So,it will have risen by a distance 2x .

The work done to lift this infinitesimally small element of length dx is

  dW=weight⋅distance=2.5×dx×2x=5xdx

The total work done is the integral of this infinitesimally small work from x=0 (at the mid-point) to x=length2=5 (at the bottom)

So

  W=∫05dw=∫055xdx

  =5x22]05=(5×252)−0

  =62.5

Therefore, the total work done is 62.5 lb⋅ft .