A sphere of moment of inertia 'I' and mass 'm' rolls down on an inclined plane without slipping its K.E. of rolling is

Options

A. `I omega + mv`
B. `0.5 mv^(2)`
C. `0.5 I omega^(2)`
D. `0.5 I omega^(2)+0.5 mv^(2)`

Answer

D

Explanation

`K. E_("Roll")=K.E._("rotation")+K.E._("translation")`
`= (1)/(2)I omega^(2)+(1)/(2)mv^(2)=0.5I omega^(2)+0.5 mv^(2)`