A coin resting on a rotating turntable just begins to slip when positioned 4 cm from the centre. If the turntable's angular velocity is doubled, the coin will just slip at a distance of

Step-by-step solution

The condition for the coin to just slip on the rotating turntable is that the required centripetal force is provided by the maximum static friction. m r ^2 = m g r = g ^2 This implies that r 1 ^2 . Let the initial angular velocity be ₁ = and the initial distance be r₁ = 4 cm . When the angular velocity is doubled, ₂ = 2 . Using the proportionality r₁ ₁^2 = r₂ ₂^2 , we get: 4 ^2 = r₂ (2 )^2 4 ^2 = r₂ 4 ^2 r₂ = 1 cm