Question

A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the center. If the angular velocity of the turntable is doubled it will just slip at a distance of
(a) 1 cm
(b) 2 cm
(c) 4 cm
(d) 8 cm

Answer 1

Answer ⇒ Option (a). 1 cm.

Explanation/Mathematical Proof ⇒ When the coin which is placed in the tumble is rotated then the Frictional force will try to balance it, and provide the necessary centripetal force which will always be less than or equal to frictional force. If if becomes greater than the Friction the coin will fall from tumble.

∴ f ≥ mv²/r

v ≤ √(μrg)

This is the maximum velocity to be on tumble so that coin does not fall.

Now, In the Given case,  

Original angular velocity = ω, new angular velocity = 2ω  

Initial radius = 4 cm. New Radius = ?

Mass of the coin is m.

∴ mr₁ω² = mr₂ω₀²

∴ r₂ = 1 cm.

Hope it helps.