Laws Of Motion Question 14
Question 14 - 2024 (31 Jan Shift 1)
A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :
(1) $\frac{\mu g}{\mathrm{r}}$
(2) $\sqrt{\frac{\mathrm{r}}{\mu \mathrm{g}}}$
(3) $\sqrt{\frac{\mu g}{r}}$
(4) $\frac{\mu}{\sqrt{\mathrm{rg}}}$
Show Answer
Answer: (3)
Solution:
$\mathrm{N}=\mathrm{mg}$
$\mathrm{f}=\mathrm{m} \omega^{2} \mathrm{r}$
$\mathrm{f}=\mu \mathrm{N}$
$\mu \mathrm{mg}=\mathrm{mr} \omega^{2}$
$\omega=\sqrt{\frac{\mu g}{r}}$
