A hollow sphere is released from the top of an inclined plane of inclination `theta` and length `L`. If a hollow sphere rolls without slipping, what will be its speed when it reaches the bottom?

Explanation

In pure rolling mechanical energy is conserved.
By the conservation of mechanical energy between the top and the bottom of incline
`K_(1)+U_(1)=K_(2)+U_(2)`
`0+mgh=(1)/(2)mv^(2)+(1)/(2)Iomega^(2)+0`
`mgLsintheta=(1)/(2)mv^(2)+(1)/(2)xx(2)/(3)mr^(2)((v)/(r))^(2)`
`=(5)/(6)mv^(2)`
`v=sqrt((6gLsintheta)/(5))`
OR
`v=sqrt((2gh)/(1+(k^(2))/(R^(2))))=sqrt((2gLsintheta)/(1+(2)/(3)))=sqrt((6)/(5)gLsintheta)`