Circular MotionMedium
Question
A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5rad/s$. The coefficient of friction between the drum's inner wall surface and mass is $\_\_\_\_$ . (Take $g = 10\text{ }m/s^{2}$ )
Options
A.0.1
B.0.5
C.0.7
D.0.3
Solution
Sol. [Key Concept: For sticking: $\mu\ m\omega^{2}R \geq \ mg \Rightarrow \ \mu_{\min} = g/(\omega^{2}R)$.]
$${N = m\omega^{2}R }{f_{s} = mg }{f_{s} \leq f_{\mathcal{l}} }{mg \leq \mu N }{mg \leq \mu m\omega^{2}R }{\mu \geq \frac{g}{\omega^{2}R} }{\mu_{\text{min}\text{~}} = \frac{g}{\omega^{2}R} = \frac{10}{10^{2} \times 1} = 0.1 }$$
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