A solid sphere is rolling without slipping on a horizontal surface. The ratio of its rotational kinetic energy and translational kinetic energy is:

CONCEPT:

Kinetic energy (K.E): 

• The energy possessed by a body by virtue of its motion is called kinetic energy.
• The expression for kinetic energy is

Where m = mass of the body and v = velocity of the body

Rotational Kinetic energy (KE):

• The energy, which a body has by virtue of its rotational motion, is called rotational kinetic energy.
• A body rotating about a fixed axis possesses kinetic energy because its constituent particles are in motion, even though the body as a whole remains in place.
• Mathematically rotational kinetic energy can be written as

Where I = moment of inertia and ω = angular velocity.

EXPLANATION:

• Moment of inertia of the solid sphere about an axis passing through center and perpendicular to its plane is given by -

• The rotational kinetic energy of the solid sphere is given by 

       ------- (1)

• The translational kinetic energy of the solid sphere is given by 

        ------- (2)

On dividing equation 1 and 2, we get