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.

A uniform solid sphere is rolled up a fixed rough inclined surface wit

1.	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.
Answer» Solution :When there is no slip between the INCLINE and the sphere, mechanical energy can be conserved. INITIAL kinetic energy of the sphere `=(1)/(2)"mu"^(2)+(1)/(2)I_(cm)omega^(2)=(1)/(2)"mu"^(2)(1+(2)/(5))=(7)/(10)"mu"^(2)` Final gravitatonal POTENTIAL energy with respect to the initial position is mgh. Therefore, MAXIMUM height reached is `(7u^(2))/(10g)`.