IIT JEE , AIEEE Forum - Physics , Mechanics - gravitational potential energy of a chain with one end tied to a sphere

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Consider an element on the chain subtending an angle of d

at the center of the sphere. The potential energy of the element wrt the horizontal level of sphere's center is
dU = {(m/l)Rd

} g Rcos

where

is the angle made by the line joining the element and vertical
U = ₀

^L/R {(m/l)Rd

} g Rcos

Evaluate the integral to get the answer

Now similarly find the PE of the chain for the situation when the chain has slid an angle

.
Apply energy conservation to get the second part

At any arbitray moment after the chain has started moving, find the KE, from this you get velocity and from there dv/dt

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