Question

a solid cylinder rolls down an inclined plane which has friction sufficient to prevent sliding . the ratio of rotational energy to total kinetic energy​

Answer 1

1:3 is the ratio of rotational energy to total kinetic energy​.

Explanation:

As we know,

Moment of inertia in a solid cylinder = I = mR^2/2

where m = mass of the cylinder, R = radius of the cylinder.

A.T.Q.

The solid cylinder rolls down an inclined plane, the P(Potential energy) at the upper part of the cylinder would be converted into K.E.(Kinetic Energy) at the inclined plane's bottom on arrival.

So,

Total Kinetic Energy(K.E.) = Translational Kinetic Energy + Rotational Kinetic Energy

Since,

Translational Kinetic Energy = 1/2 mv^2

Rotational Kinetic Energy = 1/2 I w^2

= 1/2(mR^2/2) (v^2/R^2)                                (∵v = radius * angular velocity(w))

= 1/4 mv^2

Total Kinetic Energy = 1/4 mv^2 + 1/2 mv^2

= 3/4mv^2

So,

Rotational Kinetic Energy/Total Kinetic Energy = (1/4 mv^2 ) ÷ 3/4mv^2

= 1/3

or

1:3

Thus, 1:3 is the ratio of rotational energy to total kinetic energy​

Learn more: Kinetic Energy

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