A sphere rolls down in an inclined plane without slipping. The percentage of translational energy in its total energy is

Options

A. `29.6%`
B. `33.4%`
C. `71.4%`
D. `50%`

Answer

C

Explanation

Rotational `K.E .E_("rot")=(1)/(2) omega^(2)=(1)/(2)((2)/(5)MR^(2)) omega^(2)=(1)/(5)MR^(2) omega^(2)`
Translational K.E `(E_("trans"))=(1)/(2)Mv^(2)=(1)/(2)MR^(2)omega^(2)`
`E_("rot")=E_("rot")+E_("trans") =(1)/(5) MR^(2)+(1)/(2) MR^(2) omega^(2)=(7)/(10) MR^(2) omega^(2)`
`%"of" E_("trans")=(E_("trans"))/(E_("Tot"))xx100%=(5)/(7)%=71.4%`