A uniform solid sphere is rolled up a fixed rough inclined surface with an initial speed of u. Assuming that there is no slip find the maximum height reached by the sphere over the incline.

Explanation

When there is no slip between the incline and the sphere, mechanical energy can be conserved.
Initial kinetic enregy of the sphere
`= (1)/(2) m u^(2)+(1)/(2)I_(cm)omega^(2)=(1)/(2)m u^(2)(1+(2)/(5))=(7)/(10)m u^(2)`
Final gravitational potential energy with respect to the initial position is mgh.
Therefore, maximum height reached is `(7u^(2))/(10g)`.