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A uniform round body of radius R and ma...

A uniform round body of radius `R` and mass `m` and its moment of inertia about centre of mass `O` is `I_(cm)` is given. A force `F` is applied at a height `h` above the centre of the round body. Find the height `h` at which force should be applied so that it rolls without friction.

Text Solution

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For Newton's law in horizontal direction
`F=ma_(cm)`……..`(i)`
Torque about `O`
`Fh=I_(cm)alpha`…….`(ii)`
For pure rolling
`a_(cm)=R alpha`……….`(iii)`
Solving the three equations gives
`h=(I_(cm))/(mR)`
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