A solid cylinder of mass m and radius r starts rolling down an inclined plane of inclination `theta`. Friction is enough to prevent slipping. Find the speed of its centre of mass when its centre of mass has fallen a height `h`.

Explanation

Considering the two shown position of the cylinder. As it does not slip hence total mechanical energy will be conserved.
energy at position 1 is `E_(1)=mgh`
Energy at position 2 is `E_(2)=(1)/(2)mv_(COM)^(2)+(1)/(2)I_(COM)omega^(2)`
`(v_(COM))/(r)=omega` and `I_(COM)=(mr^(2))/(2)`
`impliesE_(2)=(3)/(4)mv_(COM)^(2)`
From conservation of energy `E_(1)=E_(2)` or `mgh=(3)/(4)mv_(COM)^(2)`
`impliesv_(COM)=sqrt((4)/(3)gh)`