Question

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its centre with a uniform angular speed $2{\text{rad s}}^{-1}$. The radius of the disc is $50\text{cm}$. Find the minimum coefficient of friction between disc and coin so that the coin does not slip ($g=10{\text{ms}}^{-2}$)

• A. $0.1$
• B. $0.2$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is B $0.2$

Coin is at rest on disc. This means that the static frictional force on the coin provides the centripetal force for circular motion.
i.e $f=m{\omega }^{2}r$

Required friction force should be less than limiting value.

$f\le f_L\Rightarrow m{\omega }^{2}r\le \mu mg$
$\Rightarrow \mu \ge \frac{{\omega }^{2}r}{g}=\frac{2^2\times 50/100}{10}$
$\Rightarrow \mu \ge 0.2$