The speed of a uniform solid sphere after rolling down from rest without slipping along a fixed inclined plane of vertical height (h ) is

Step-by-step solution

If (v ) is the speed of solid sphere when it reaches at point (O ), then by the law of conservation of energy, ( array ll & m g h= 1 2 I ^2+ 1 2 m v^2 & = 1 2 2 5 m R^2 ( v R )^2+ 1 2 m v^2 & m g h= 1 5 m v^2+ 1 2 m v^2 & g h= v^2 5 + v^2 2 g h= 7 v^2 10 & v^2= 10 g h 7 v= 10 g h 7 array )