If a sphere is rolling, the ratio of 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

Translational energy `=1/2 Mv^(2)`
Total kinetic energy `=1/2 Mv^(2)+1/2 I omega^(2)`
`=1/2 Mv^(2)+1/2xx2/5 MR^(2)xx(v^(2))/(R^(2))`
`=1/2 Mv^(2)+1/5Mv^(2)`
`=((5+2)/10)Mv^(2)=7/10 Mv^(2)`
`("Translational energy")/("Total kinetic energy")=1/2 Mv^(2)xx10/(7Mv^(2))=5/7`
Translation energy `:` Total kinetic energy `=5:7`