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

Options

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

Explanation

Total kinetic energy `E _(energt")+ E _(rot) = (1)/(2) mv ^(2) + (1)/(2) I omega ^(2)`
`= (1)/(2) mv ^(2) + ((2)/(5) mr ^(2)) omega ^(2)`
`(1)/(2) mv ^(2) + (1)/(5) mv ^(2) = (7)/(10) mv ^(2)`
`therefore (E _("energy"))/( E _("total"))= ((1)/(2) mv ^(2))/((7)/(10) mv ^(2)) = (5)/(7)`