A thin hollow cylinder open at both ends
(i) Slides without rotating
(ii) Rolls without slipping, with the same speed.
The ratio of kinetic energies in the two cases is

Options

A. `1:1`
B. `4:1`
C. `1:2`
D. `2:1`

Answer

C

Explanation

Translational K.E. =`1/2mv^(2)`
K.E. of rolling body= K.E. of translation+ K.E. of rotation
`E=1/2mv^(2)+1/2Iomega^(2)=1/2mv^(2)+1/2mR^(2).omega^(2)`
`E=1/2mv^(2)+1/2mv^(2)=mv^(2)`
`therefore("Translation K.E.")/(.Total K.E.")=1/2.(mv^(2))/(mv^(2))=1/2`