A man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with constant angular velocity of $5$ $rad/sec.$ At what distance from centre should he stand so that he does not slip on the disc?
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To prevent slipping, centripetal force $\leq $ frictional force$:$
$F=m R_{\max } \omega^{2}$
$F \leq f \Rightarrow F \leq \mu N[N=m g]$
$\Rightarrow m R_{\max } \omega^{2} \leq \mu m g$
$\Rightarrow R_{\max } \leq \frac{\mu g}{\omega^{2}}=\frac{0.5 \times 5}{5^{2}}$
$\Rightarrow R_{\max } \leq 0.2 m$
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