Question

a thin ring of mass m and radius r rolls down an inclined plane from height h without slipping .when it reaches the bottom ,speed of its centre of mass is

Answer 1

Use conservation of energy.

Initial total energy = mgh

Final total energy = 1/2mv^2[1 + β]
[Here β = k²/r². For ring about it’s central axis β = 1]

Equate both

For further solution refer image attached.