A gramphone record is revolving with an angular velocity `omega`. A coin is placed at a distance `R` from the centre of the record. The static coefficient of friction is `mu`. The coin will revolve with the record if

Options

A. `r ge (mu g)/(omega^(2))`
B. `r = mu g omega^(2)`
C. `r lt (omega^(2))/(mu g)`
D. `r le (mu g)/(omega^(2))`

Answer

D

Explanation

Since , `v le sqrt(mu r g)`
`implies v^(2) le mu r g`
`implies (r omega)^(2) = mu r g`
`implies r omega^(2) le mu g implies r le (mu g)/(omega^(2))`