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A uniform solid sphere is rolled up a fi...

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.

Text Solution

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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)`.
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