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A uniform spherical sheel rolls down a f...

A uniform spherical sheel rolls down a fixed inclined plane without sliping. Find the ratio of rotational kinetic energy to translational kinetic energy as it reaches lowest point of the incline.

Text Solution

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As there is no slip,
`v=Romega` is valid and rotational kinetic energy
`K_(R)=(1)/(2)I_(cm)omega^(2)=(1)/(2)mk^(2)omega^(2)`
and translational kinetic energy
`K_(T)=(1)/(2)mv^(2)=(1)/(2)mR^(2)omega^(2)` therefore `(K_(R))/(K_(T))=(k^(2))/(R^(2))=(2)/(3)`
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