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A football of radius R is kept on a hole...

A football of radius R is kept on a hole radius r `(r lt R)` made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle `theta` from the horizontal as shown in the figure below.
The maximum value of `theta` so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

A

`sin theta=(r )/(R )`

B

`tan theta=(r )/(R )`

C

`sin theta=(r )/(2R)`

D

`cos theta=(r )/(2R)`

Text Solution

Verified by Experts

The correct Answer is:
A

`mg sin thetasqrt(R^(2)-r^(2))=mg cos thetar`
`tan theta=(r )/(sqrt(R^(2)-r^(2)))`
`sin theta=(r )/(R )`
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