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  4. A coin placed on a rotating table just slips if it is placed at a distance 4r from the centre. If we double the angular velocity of the table, then the coin will just slip when it is away from the centre at a distance equal to

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Q. A coin placed on a rotating table just slips if it is placed at a distance $4r$ from the centre. If we double the angular velocity of the table, then the coin will just slip when it is away from the centre at a distance equal to

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

$\therefore \omega =\sqrt{\frac{µ g}{r}} \, \therefore \omega \propto \frac{1}{\sqrt{r}} \, \Rightarrow r \propto \frac{1}{\omega ^{2}}$
Since $\omega $ is double thus,
$r′=\frac{4 r}{4}=r$