A hollow sphere rolls without slipping the on the horizontal surface such that its translational velocity is `v`. Find that the maximum height attained by it on an inclined surface.

Explanation

In case of pure rolling, energy is conserved, `v=romega`. Applying the energy conservation between positions (`1`) and (`2`)

`K_(1)+U_(1)=K_(2)+U_(2)`
`(1)/(2)mv_(c.m.)^(2)+(1)/(2)I_(c.m.)omega^(2)=0+mgh`
`(1)/(2)mv^(2)+(1)/(2)xx(2)/(3)mr^(2)((v)/(r))^(2)=mgh`
`(5)/(6)mv^(2)=mgh`
`h=(5v^(2))/(6g)`
OR
`(1)/(2)mv_(c.m.)^(2)(1+(k^(2))/(R^(2)))=mgh`
(`(K^(2))/(R^(2))=(2)/(3)`for hollow sphere)
`(1)/(2)mv^(2)(1+(2)/(3))=mghimplies h=(5v^(2))/(6g)`