A-Level Physics- Work

Let p be the density of the rope

Consider a small element, dm, on the rope hanging freely over the edge.

dm = pdy

Where dy is the length of the small element.

And now, define y be the vertical distance of the small element from the edge. 0<= y <= x/4

To raise the small element up on the edge, the work done = dm gy = pgydy

To find the work done to raise the remaining part of the rope, do an integration from y = 0 to y = x/4

int [0,x/4] pgydy

= pg(x^2/16)/2

= pgx^2 / 32

But px is the mass of the rope, m

So, the work done = mgx/32

The answer is D.

The naswer is option D.

Just calculate the increase in potential energy of the rope.