Q. 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
Explanation
(a) The object will slip if centripetal force acting on it is more than friction force.
$So,\ \ \ \ {mr\omega}^{2} > \mu mg$
${r\omega}^{2} \geq \mu g$
${r\omega}^{2} = constant$
$\frac{r_{1}}{r_{2}} = \left( \frac{\omega_{2}}{\omega_{1}} \right)^{2}$
$\frac{4}{r_{2}} = \left( \frac{2\omega}{\omega} \right)^{2}$
$r_{2} = 1\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.