A sphere of mass 0.5 kg and diameter 1 m rolls without sliding with a constant velocity of 5 m/s. What is the ratio of rotational KE to the total kinetic energy of the sphere ?

Options

A. `(7)/(10)`
B. `(5)/(7)`
C. `(2)/(7)`
D. `(1)/(2)`

Answer

C

Explanation

`(KE_("rot"))/(KE_("rolling"))=(k^(2)//R^(2))/(1+k^(2)//R^(2))`
`=(2//5)/(1+2//5)=(2//5)/(3//5)=(2)/(7)`