A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if
A$R \leq \frac{\mu g}{2 \omega^{2}}$
B$R \leq \frac{\mu g }{\omega^{2}}$
C$R \geq \frac{\mu g}{2 \omega^{2}}$
D$R \geq \frac{\mu g }{\omega^{2}}$
JEE MAIN 2022, Medium
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B$R \leq \frac{\mu g }{\omega^{2}}$
b $f_{s}=m \omega^{2} R$
We know that $f_{ S } \leq f _{\text {smax }}$
$m \omega^{2} R \leq \mu m g$
$R \leq \frac{\mu g }{\omega^{2}}$
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