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

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 :- ( g = 10 m / s 2 )

TestHub · Accepted Answer

At the slipping limit, friction supplies the needed centripetal force.

$μ_{s} m g = m ω^{2} r$

The limiting radius varies inversely with the square of angular speed.

$r_{2} = r_{1} (\frac{ω _{1}}{2 ω _{1}})^{2} = \frac{4 cm}{4} = 1 cm$

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