When a disc is rotating with angular velocity `omega` , a particle situated at a distance of 4 cm just begins to slip . If the angular velocity is doubled , at what distance will the particle start to slip ?

Options

A. 4 cm
B. 9 cm
C. 16 cm
D. 1 cm

Answer

D

Explanation

For the coin , centrifugi force = Frictional force
` therefore mr omega ^(2) = mu mg`
` therefore omega ^(2) = (mu g) /( r ) i.e., omega ^(2) prop (1)/(r ) `
` therefore (omega_(2)^(2))/(omega_(1)^(2))=(r_(1))/(r_(2))" " therefore ((2 omega )/(omega ))^2 = (4)/( r_(2))`
` therefore (4)/(1) = (4)/(r_(2)) " " therefore r_(2) = 1cm`