Question

A rope of 2l and a mass of m is hanging from a rigid support . The tension in the rope at a distance l/3 from the rigid support will be ?​

Answer 1

Given:

Mass of the rope = m

Length of the rope= 2l

To find:

The tension in the rope at a distance l/3 from the rigid support.

Solution:

Let us consider a small part of rope dx of mass dm which will have tension= dT due to it's weight.

dT= dmg

Where dm = m dx/ 2l

Putting the values we get:

dT = mg dx/2l

On integrating with limits from 0 to 2l-l/3 = 5l/3, we get:

T= (mg*5l)/ (3*2l) = 5mg/6

Therefore the tension in the rope will be 5mg/6.