Question

A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled the object slips when its distance from the axis of rotation is

• A. 1 cm
• B. 2 cm
• C. 4 cm
• D. 8 cm

Answer 1

The Correct Option is A

The object will slip if centripetal force
$ \le $ force of friction i.e.,
$ \frac{m{{v}^{2}}}{r}\ge \mu R $
$ m{{\omega }^{2}}r\ge \mu mg $
$ (\because v=r\omega ,R=mg) $
$ {{\omega }^{2}}r\ge \mu g $
$ r\propto \frac{1}{{{\omega }^{2}}} $
$ \frac{{{r}_{2}}}{{{r}_{1}}}={{\left( \frac{{{\omega }_{1}}}{{{\omega }_{2}}} \right)}^{2}} $
Put $ {{r}_{1}}=4\,cm,{{\omega }_{2}},{{\omega }_{2}}=2\omega $
$r_2 = 1 cm$