A chain of length

The gravitational potential energy of the chain is

The chain is released and slides down the sphere

The tangential acceleration of the chain is

Given

The length of the chain is l, mass of the chain is m, and the radius of the sphere is given as R.

Formula Used

The formula for the total energy in terms of kinetic and potential energy is given as

where

The is the total energy in terms of kinetic and potential energy, m is the mass of the object, g is the acceleration in terms of gravity and l is the length of the object, is the angle of exit.

Explanation

(a) Let the angle formed by the chain is =

The length of the chain =

Therefore, the angle is written as

The length of the chain in terms of radius is

The force derivative of the chain is given as

The potential energy is calculated as

The P.E. after integration is

(b) The kinetic energy and the potential energy of the chain is equivalent to

The initial potential energy is calculated as

The change in the potential energy is

.

(c) Now to find the tangential velocity we use the equation of

After reduction the value of the is