Two particles having masses M and m are moving in a circular path having radii R and r respectively. If their periods are same, then the ratio of their angular velocities will be

Options

A. `(R )/(r )`
B. `sqrt((R )/( r))`
C. `(r )/(R )`
D. 1

Explanation

Time period = `(2 pi R)/(v_(1)) = (2 pi r)/(v_(2))`
or, ` (v_(1))/(v_(2)) = (R )/(r )` [ where `v_(1) and v_(2)` are linear velocities ]
If the angular velocities are `omega_(1) and omega_(2)` respectively,
`v_(1) = omega_(1) R " "and v_(2) = omega_(2)r`
`therefore " "(omega_(1))/(omega_(2)) = (v_(1))/(R ) cdot (r )/(v_(2)) = (R )/(r )cdot (r )/(R ) = 1 `
The option D is correct.