Question

A block rests on a horizontal table which is executing an SHM in the horizontal plane with an amplitude a. If the coefficient of friction is m, the block just starts to slip when the frequency of oscillation is:

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

Answer 1

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

For just slipping of block
$m{\omega }^{2}a=\mu mg{\omega }^2=\frac{\mu g}{a}{\omega }^2=\sqrt{\frac{\mu g}{a}}2\pi f=\sqrt{\frac{\mu g}{a}}f=\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$