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A particle is moving with uniform speed ...

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to `R^3`. its time period of revolution will be given by :

A

`T prop R^((3)/(2))`

B

`T prop R^(2)`

C

`T prop R^((4)/(3))`

D

`T propR ^((5)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
` F prop (1)/(R_(3))`
`(K)/( R^(3)) = m omega ^(2) R rArr omega ^(2) = (K)/( m) xx (1)/( R^(4))`
`((2 pi)/( T))^( 2) = (K)/( m) xx (1)/( R^(4))`
`T^(2) prop R^(4) rArr T prop R^(2)`
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