A particle is revolving in a circle of radius R. If the force acting on it is inversely proportional to R, then the time period is proportional to

Options

A. R
B. `R^(2)`
C. `1//R`
D. `1//R^(2)`

Answer

A

Explanation

Given that the force is inversely proportional to R
i.e. `F prop (1)/(R) `
or `F=k/R " "…(i)`
or `mRw^(2)=k/R`
or `w^(2)=(K)/(mR^(2))`
`therefore w^(2) prop (1)/(R^(2))`
`implies w prop (1)/(R)`
`implies (2pi)/(T) prop (1)/(R)`
`implies T prop R`