An annular ring with inner and outer radii `R_(1) and R_(2)` is rolling without slipping with a uniform angular speed. The ratio of force experienced by the two particles situated on the inner and outer parts of the ring. `(F_(1))/(F_(2))` = …………

Options

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

Answer

A

Explanation

The centripetal force due to rolling ring,
`(mv^(2))/(r )=F`
`therefore (mr^(2)omega^(2))/(r)=F`
`therefore F=mromega^(2)`
`therefore F_(1)=mR_(1)omega^(2)`
`therefore F_(2)=mR_(2)omega^(2)`
`therefore (F_(1))/(F_(2))=(R_(1))/(R_(2))`