Question

A circular rope of weight w and radius r/2 is resting

Answer 1

Given: The full question is A circular rope of weight W and radius r = R/2 is resting on a smooth sphere of radius R.

To find: Find the tension in rope.

Solution:

• Now we have given the weight as W and radius as R/2

• Now lets take a small segment of the rope with an angle dθ in the circle of radius r.

• Angle between plane of rope and line joining center of sphere to edge of rope is 60 degree.

• So balancing it, we get:

                N sin(60) = mgdθ / 2π ..............(i)

                N cos(60) = 2T sin(dθ / 2)

                N cos(60) = Tdθ .................(ii)

• Now dividing (i) and (ii), we get:

               √3 = mgdθ / 2π / Tdθ

               T = mg / 2π√3

               T = W/√12π

Answer:

             So the tension in the rope is W/√12π.