Question

A block rests on a horizontal table which is executing SHM in the horizontal plane with an amplitude ${}^{\prime }{a}^{\prime }$. If the coefficient of friction is ${}^{\prime }{\mu }^{\prime }$, then the block just starts to slip when the frequency of oscillation is :

• A. $\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$
• B. $\sqrt{\frac{\mu g}{a}}$
• C. $\frac{1}{2\pi }\sqrt{\frac{a}{\mu g}}$
• D. $\sqrt{\frac{a}{\mu g}}$

Answer 1

The correct option is A $\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$

For the block is about the slip, $\mu g={\omega }^{2}a$
or $\Rightarrow \omega =\sqrt{\frac{\mu g}{a}}$
$2\pi n=\sqrt{\frac{\mu g}{a}}\Rightarrow n=\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$