A coin is placed on a horizontal turntable rotating at `33(1)/(3)` rpm. The coin revolves with the table without slipping provided the coin is not more that 10 cm away from the axis. How far from the axis can the coin be placed so that it revolves with the table without slipping if the turntable rotates at 45 rpm ?
( g = 980 cm`cdot s^(-2)` )

Explanation

The magnitude of the limiting frictional force between the body and the disc gives the maximum value of centripetal force. So, if the body of mass m rotates along a circular path of maximum radius r with angular velocity `omega`, then the limiting frictional force,
f = `m omega^(2)` r
In the first case of the given problem, f = `m omega_(1)^(2) r_(1)`
and in the second case, f = m`omega_(2)^(2) r_(2)`
`therefore " " m omega_(1)^(2) r_(1) = m omega_(2)^(2) r_(2)`
or, `r_(2) = (omega_(1)^(2))/(omega_(2)^(2)) xx r_(1) = ((100)/(3 xx 45))^(2) xx 10 = 5.5` cm.