Question

A coin placed on a rotating turntable just slips, if it is placed at a distance of $8\, cm$ 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 $F=m r \omega^{2}$
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, $r_{1}=8\, cm,\, \omega_{1}=\omega,\, \omega_{2}=2\, \omega$
$\therefore r_{2}=\frac{8 \times \omega^{2}}{(2 \omega)^{2}}$
$=\frac{8}{4}=2\, cm$