Question

A coin placed on a rotating turntable just slips, if it is placed at a distance of $8cm$ from the centre. If angular speed 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: (B)

A body placed on a non-inertial frame of reference which is rotating about its axis, experiences a centrifugal force.
It is given by $F=mr{\omega }^2$
where $r$ is radius of circle, $m$ is mass and co is angular speed.
$\therefore \frac{F_1}{F_2}=\frac{r_1{\omega }_1^2}{r_2{\omega }_2^2}$
Since, $F_1=F_2$
$\Rightarrow r_1{\omega }_1^2=r_2{\omega }_2^2$
$\Rightarrow r_2=\frac{r_1{\omega }_1^2}{{\omega }_2^2}$
Given, $r_1=8cm,{\omega }_1=\omega ,{\omega }_2=2\omega$
$\therefore r_2=\frac{8\times {\omega }^2}{(2\omega {)}^2}$
$=\frac{8}{4}=2cm$