Tension in a chain partly on a smooth sphere

[mooncrater]

Homework Statement

The question says
A chain of mass per unit length k and length 1.5 m rest on a fixed smooth sphere of radius R= 2/π m
. Tension in the thread is asked.The question figure is attached.

Homework Equations

N/a

The Attempt at a Solution

I think that the tension has to balance two types of forces :
1) rightward force of part AC(touching)
2)downward force of part CB(hanging)
Finding first type of force:
Using Fbd(attached) of small part taken in touching part
Then Ncos(theta)=(dm)g
→ N=(dm)g/cos(th.)...(1)
Length of that part =R(d(th.))
mass of that small part =Rk(d(th.))
Using Fbd rightward force on the small part =Nsin(th.)=(dm)g(tan(th.))
=Rkgtan(th.)(d(th.))
Now if I want to integrate it , i would have to use limits from 0 to π/2
BUT tan (th.) is not integrable b/w 0 to π/2 . So what's wrong with my answer ?

 

[BvU]

I'm missing something in your force balance for the little chunk of chain. I see an N and an mg and they clearly don't balance. What force could possibly complete the picture ?

 

[mooncrater]

I'm missing something in your force balance for the little chunk of chain. I see an N and an mg and they clearly don't balance. What force could possibly complete the picture ?

It could have been friction BUT the sphere is smooth so , what can be the force (you are talking about ) left out that balances the tension of the thread ?

 

[haruspex]

It could have been friction BUT the sphere is smooth so , what can be the force (you are talking about ) left out that balances the tension of the thread ?

But you don't have the tension in the chain in the equation. Indeed, that's what's missing. Remember, it will not be constant along the the chain.

 

[nil1996]

You have to consider the tension on both sides of the element along the tangential direction!