Question

A uniform rope of mass m and length l is fixed at its upper end vertically from a rigid support

Answer 1

Hey mate i think ur question is incomplete .plz complete ur question and post it again.

Answer 2

Complete Question: A uniform rope of mass m and length l is fixed at its upper end vertically from a rigid support. Then the tension in the rope at the distance l from the rigid support is?

Answer:

Tension, T = Mg/L × (L-l)

Explanation:

[Refer to the attached image 1 to understand the case]

[Method 1]

Note; In order to tackle such questions, you need a good level of understanding and your basic concepts regarding the case must be cleared already.

Now, Given;-

         Length, L = M

so, 1 unit length has mass = M/L

Then;-

[Refer to attached image 2 to understand the free body diagram of lower part of the rope]

     (L- l) length has mass = M/L × (L- l)

Now, since rope and its mass all at rest, its net force must be 0. Then, in this case tension will be equal to force acting on opposite direction. Here;-

      M'g = M/L ( L- l)g

But,   T = M'g

So,    T = M/L (L- l)g

[Method 2]

( Based on personal Assumptions with case )

We can quite clearly see that we don't have any fixed value of l. That means its variable. Let us tackle the question by assuming values on our own. Let's see if we can handle this.

Now, this method is useful when dealing with questions containing options during which this method will help wipe out the wrong options.

There is nothing to explain for this method, its just a statement with some variables. This is my own discovery after hours of toiling on such problems.

So, just assume that l = L. Now, the option which cancels out completely giving tension = 0 will be the correct answer. ( You may not get this but this is a gem of all the unique methods we rarely use. Please, ignore this method if question has no option. )

Hope it helps! ;-))