Question

A horizontal turn table is rotating at some angular velocity. An object just slips when it is placed at a distance $4 \, cm$ from the axis of rotation. Now, the angular velocity of the turn-table is doubled. The object will slip when it's distance from the axis of rotation is:

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

Answer 1

Answer: (A)

The object will slip if centripetal force ≥ force of friction
$mr\omega ^{2}>\mu mg$
$r\omega ^{2}\geq \mu g$
$r\left(\omega \right)^{2}\geq constant,or \, \left(\frac{r_{1}}{r_{2}}\right)=\left(\frac{\left(\omega \right)_{2}}{\left(\omega \right)_{2}}\right)^{2}$
$\frac{4 \, c m}{r_{2}}=\left(\frac{2 \omega }{\omega }\right)^{2}\therefore r_{2}=1 \, cm$