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As shown in the figure, a person of mass 'm' remains stuck to the wall of rotating rotor. What should be the minimum value of angular velocity $\omega$ [coefficient of friction between wall and man is $\mu$ ]

Option: 1
$\sqrt{\frac{\mu g}{R}}$

Option: 2
$\sqrt{\frac{g}{R}}$

Option: 3
$\sqrt{\frac{g}{\mu R}}$

Option: 4
$\sqrt{\mu g R}$

Answers (1)

best_answer

Sticking of Person with the wall of Rotor(Death well) -

F = weight of person (mg)

$\mu R=mg$

$\mu F_{c}=mg$

$\mu m \omega_{min}^{2}r=mg$

$\therefore\ \omega_{min}=\sqrt{\frac{g}{\mu r}}$

Where F = friction force

F_c= centrifugal force

= minimum angular velocity

$\mu=$ coefficient of friction

r = radius of Rotor

From the figure

$\\f_r = mg \\\mu N = mg\;\;[f_r = \mu N] \\\mu F_c = mg\;\;[As\;N=F_c]$

$\mu m \omega_{min}^2R = mg \Rightarrow \omega_{min} = \sqrt{\frac{g}{\mu R}}$

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manish

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