Question

A solid sphere having mass m and radius r rolls
down an inclined plane. Then its kinetic energy is
(1) 5/7rotational and 2/7translational
12) 2/7rotational and 5/7translational
-3) 2/5rotational and 3/5translational
4) 1/2rotational and 1/2
translational

Answer 1

Answer:

The kinetic energy is 1/2rotational and 1/2

translational.

Explanation:

*m = Mass of the sphere

*r = Radius of the sphere

*I = Moment of inertia of the sphere = $\dfrac{2mr^2}{5}$

*K.E. =  Total kinetic energy of the sphere

*$\omega$ = Rotational velocity of the body

*v = Translational velocity of the body.

we have,

K.E. = Translational K.E. + Rotational K.E.

K.E. = $K.E. = \dfrac{mv^2}{2}+\dfrac{I\omega^2}{2}$

The above equation shows that, the rotational and kinetic energy contributes equal parts in the total energy.

The correct option is (4).

Answer 2

Answer:

2/7 rotational 5/7 translational

Explaination:

*Click pic to view*