A solid sphere of mass m and radius r is rolling on a horizontal surface. What ratio of total energy of the sphere is:
Kinetic energy of rotation ?
Kinetic energy of translation ?

Explanation

Mass of sphere = m radius = r
Moment of inertia = `(2)/(5) mr^(2)`
Total energy `= K_(R)+K_(r)`
`K_("total") = (1)/(2)Iomega^(2)+(1)/(2)mv^(2)=(1)/(2)xx(2)/(5)mr^(2) (v^(2)/(r^(2)))+(1)/(2)mv^(2)`
`(because v =romega)`
`K_("total") = (1)/(2)((7)/(5))mv^(2)`
Fraction of kinetic energy of rotation
`(K_(R))/(K_("total"))=((1)/(2)((2)/(5))mv^(2))/((1)/(2)((7)/(5))mv^(2))=(2)/(7)`
Fraction of kinetic energy of translation
`=(K_(T))/(K_("total"))=((1)/(2)mv^(2))/((1)/(2)((7)/(5)mv^(2)))=(5)/(7)`