Question

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. $R\le \frac{\mu g}{2{\omega }^2}$
• B. $R\le \frac{\mu g}{{\omega }^2}$
• C. $R\ge \frac{\mu g}{2{\omega }^2}$
• D. $R\ge \frac{\mu g}{{\omega }^2}$

Answer 1

Answer: (B)

For beaker to move with disc

$f_s=m{\omega }^{2}R$
We know that $f_s\le f_{s\max }$
$m{\omega }^{2}R\le \mu mg$
$R\le \frac{\mu g}{{\omega }^2}$