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A coin placed on a rotating turntable just slips when it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of:

1. 1 cm
2. 2 cm
3. 4 cm
4. 8 cm

Correct answer: 1 cm

Solution

For a coin on a rotating turntable, the maximum static friction supplies centripetal force: $\mu mg=m\omega^2 r$. Thus $r\propto 1/\omega^2$. If angular velocity is doubled, the slipping radius becomes one-fourth.

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