A sphere of radius r is rolling without sliding. What is ratio of rotational K.E and total K.E associated with the sphere ?

Options

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

Answer

b

Explanation

`E_("Tot") = E_("trans") + E_("rot") = (1)/(2) mv^(2) + (1)/(2) I omega^(2)`
`= (1)/(2) mv^(2) + (1)/(2) xx (2)/(5) mr^(2). (v^(2))/(r^(2))`
`=(1)/(2) mv^(2) + (2)/(10)mv^(2) = (7)/(10) mv^(2)`
`(E_("rot"))/(E_("Tot"))=((1)/(5)mv^(2))/((7)/(10) mv^(2)) = (2)/(7)`