Question

A coin placed on a rotating turn table just slips if it is placed at a distance of $20cm$ from the centre. If the angular velocity of the turn table is doubled, the coin will just slip at a distance of:

• A. $40cm$
• B. $20cm$
• C. $10cm$
• D. $5cm$

Answer 1

The correct option is D $5cm$

For the coin to be in equilibrium we have

$\mu mg=mr{\omega }^2$

Thus we get

$r\propto \frac{1}{{\omega }^2}$

Thus,

$\frac{r_1}{r_2}=\frac{{\omega }_2^2}{{\omega }_1^2}=\frac{4}{1}$

Thus we get

$r_2=\frac{20}{4}=5cm$