A circular dise in rolling down in an inclined plane without slipping. The percentage of rotational energy in its total energy is

Options

A. `66.61%`
B. `33.33%`
C. `22.22%`
D. `50%`

Answer

B

Explanation

Rotational `K.E=(1)/(2)lomega^(2)=(1)/(2)((1)/(2)MR^(2)) omega^(2)=(1)/(4) MR^(2) omega^(2)`
Translational `K.E.=(1)/(2) MV^(2)=(1)/(2)M(R omega)^(2)=(1)/(2) MR^(2) omega^(2)`
Total kinetic energy `=E_("rot")+E_("trans")=(1)/(4)MR^(2) omega^(2)=(3)/(4) MR^(3)MR^(2) omega^(2)`
`% "of" E_("rot") =(E_("rot"))/(E_("rot"))xx100%=33.33%`