question_answer

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 |li, the block just starts to slip when the frequency of oscillation is:

A) \[\sqrt{\frac{\mu g}{a}}\]                     

B) \[\frac{1}{2\pi }\sqrt{\frac{a}{\mu \operatorname{g}}}\]

C) \[2\pi \sqrt{\frac{\mu g}{a}}\]                

D) \[\frac{1}{2\pi }\sqrt{\frac{\mu \operatorname{g}}{\operatorname{a}}}\]

Correct Answer: D

Solution :

Block of mass 'm' rest on a horizontal plane frictional force is the restoring force which try to bring back block to the mean position. \[{{\omega }^{2}} a \ge  \mu mg\] \[\omega   \ge  \sqrt{\frac{\mu \operatorname{g}}{m}}\] \[2\pi f \ge  \sqrt{\frac{\mu g}{a}}\] \[\operatorname{f}  \ge \frac{1}{2\pi } \sqrt{\frac{\mu \operatorname{g}}{a}}\]