Question

a solid spherical ball rolls down on an inclined plane.
the ratio of rotational energy to total kinetic energy is

Answer 1

Let the angle of the incline be = Ф.
Radius of the solid ball = R
Velocity of the ball = v
Angular velocity = ω
Friction = 0  Assumption
mass of the ball = m
Moment of inertia of the ball about a diameter = 2/5 * m R²
As the ball rolls and does not skid, v = rω

Rotational KE = 1/2 * I ω² = 1/5 m R² ω² = 1/5 m v²
Translational KE = 1/2 m v²
Total KE = 7/10 m v²

Rotational KE :  total KE = 1/5 :  7/10  =  2 : 7

We can find the velocity from the distance traveled:
If the solid ball travels a distance of L down the plane, then 
   PE lost = m g L/sinФ = 7/10 m v²
    v² = 10gL / (7 sinФ)

Answer 2

Answer:

A sphere of moment on inertia I rolls down an inclined plane without slipping. The ratio of the rotational

kinetic energy to the transitional kinetic energy is nearly

Explanation: