What Is the Tangential Acceleration of a Chain Sliding Down a Sphere?

[randommanonea]

A chain of length 'l' and mass 'm' lies on the surface of a smooth sphere of radius 'R' > 'l', with one end tied to the top of the sphere.

(a) Find the gravitational potential energy of the chain with reference level at the center of the sphere.

(b) Find the tangential acceleration dv/dt of the chain when the chain starts sliding down.

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I was able to do the (a) part, which is a matter of simple integration and my answer came out to be {m R^2 g sin(l/R)}/l

Can someone please help me out with the (b) part.

 

[zorro]

Hi Randommanonea,
Welcome to PF!

To find dv/dt, try to use the principle of conservation of energy i.e. find out the kinetic energy when the chain slides by an angle say ϑ.
Then differentiate the equation to get an expression for dv/dt, use v=rdϑ/dt for simplification (assuming that the sphere does not rotate).

Feel free to ask any doubt in the above steps.

 

[randommanonea]

I got my answer as :

Rg{1-cos(l/R)}/l


Is it correct ?

 

[zorro]

Yes its correct