A solid sphere is given a kinetic energy E. What fraction of kinetic energy is associated with rotation

Options

A. `3//7`
B. `5//7`
C. `1//2`
D. `2//7`

Answer

D

Explanation

Linear kinetic energy `=(1)/(2)mv^(2)`
Rotational kinetic energy `=(1)/(2)l omega^(2)=(1)/(2)((2)/(5)mr^(2))(v^(2))/(r^(2))=(1)/(5)mv^(2)`
`"Total KE, E"=(1)/(2)mv^(2)+(1)/(5)mv^(2)=(7)/(10)mv^(2)`
`"Required fraction "=((1)/(5)mv^(2))/((7)/(10)mv^(2))=(1)/(5)xx(10)/(7)=(2)/(7)`