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A particle 'P' is moving on a circular p...

A particle `'P'` is moving on a circular path under the action of only one force action always toward the fixed point `'O'` on the circumference. Find the ratio of `(d^(2)theta)/(dt^(2))` & `(("d"theta)/(dt))^(2)`

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The correct Answer is:
2
`a_(1)=(F)/(m)sin theta rArr (Rd^(2)(2 theta))/(dt^(2))=(F)/(m) sin theta`
`(d^(2) theta)/(dt^(2))=(F sin theta)/(2 mR)` ....(1)
`a_(c) =(F)/(m) cos theta,R[(d)/(dt)(2 theta)]^(2)=(F)/(m) cos theta`....(ii)
`(((d^(2)theta)/(dt^(2))))/(((d theta)/(dt))^(2))=2 tan theta =2`
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