If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by

Options

A. `7:10`
B. `2:5`
C. `10:7`
D. `5:7`

Answer

D

Explanation

Total kinetic energy
`E=_("trans")+E_("not")=1/2mv^(2)+1/2lomega^(2)`
`=1/2mv^(2)+1/2xx(2/5mr^(2))omega^(2)=1/2mv^(2)+1/5mv^(2)=7/10mv^(2)`
`therefore(E_("trans"))/(E_("total"))=(1/2mv^(2))/(7/10mv^(2))=5/7`