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

Answer: (A)

1 cm

Answer 2

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 ${{r}_{1}}=4\,cm,{{\omega }_{2}},{{\omega }_{2}}=2\omega$
$r_2 = 1 cm$