Ncert Exercises & Solutions

5.39 A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

H e r e, F_{N} = m g

C e n t r i p e t a l f o r c e = m r ω^{2}

T h e m a n i s s t u c k t o t h e w a l l a f t e r t h e f l o o r i s r e m o v e d .

I f, μ \geq \frac{F_{N}}{F_{C}}

\Rightarrow F_{N} \leq μ F_{C}

\Rightarrow m g \leq μ m r ω^{2}

\Rightarrow ω^{2} \geq \frac{g}{μ r}

\Rightarrow ω \geq \sqrt{\frac{g}{μ r}}

$The minimum angular speed is given as,$
$ω_{\min} = \sqrt{\frac{g}{μr}}$
$= \sqrt{\frac{10}{0.15 \times 3}} = 4.71 rad / s$

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