Question

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

• A. $1cm$
• B. $2cm$
• C. $4cm$
• D. $4cm$

Answer 1

The correct option is A $1cm$

Given, distance of the coin from the centre in first case, $r_1=4cm$
Let angular velocity of the turn table be $\omega$,
So, when the coin is just on the verge of slipping,
$F=m{\omega }_1^2{r}_2=m{\omega }_2^2{r}_2\frac{{\omega }_1^2{r}_1}{{\omega }_2^2{r}_2}=1r_2=\frac{{\omega }_1^2{r}_1}{{\omega }_2^2}{r}_2=\frac{\omega \times 4}{4\omega }=1cm$