Question

When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.

Options

• 1 : 7

• 1 : 2

• 1 : 1

• 5 : 7

Answer 1

When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is 5 : 7.

Explanation:

`(K_r)/(K_R) = (1/2mv^2)/(1/2mv^2 + 1/2Iω^2)`

`= (1/2mv^2)/(1/2mv^2 + 1/2xx2/5MR^2 xxv^2/R^2)`

`= 1/ (1+ 2/5) = 5/7 or 5:7     ....{{:(I = 2/5 MR^2 and),(v = = Rω):}`