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Working with a Rolling Sphere on Incline

As shown in the figure a uniform solid sphere rolls on a horizontal surface at 30 m/s and then rolls up the incline. If frictional losses are negligible, what will be the value of its height when the it stops ?

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The total energy remains constant through the process. The rotational and translational kinetic energy of the body will be changed to potential energy when the sphere stops. Hence,

(1/2) m V^2 + (1/2) I w^2 = m g ...

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Very detail answer with easy to understand steps. It will enable you to do similar problems yourself.