question_answer

A body of mass m is placed on a rough surface with coefficient of friction \[\mu \] inclined \[\theta \]If the mass is in equilibrium, then:

A) \[\theta ={{\tan }^{-1}}\mu \]              

B) \[\theta ={{\tan }^{-1}}\frac{1}{\mu }\]

C) \[\theta ={{\tan }^{-1}}\frac{m}{\mu }\]                      

D) \[\theta ={{\tan }^{-1}}\frac{\mu }{m}\]

Correct Answer: B

Solution :

[a] At equilibrium \[mg\sin \,\theta =\mu \,\,mg\cos \theta \] \[\mu \,\,\tan \theta \] \[\theta \,{{\tan }^{-1}}(\mu )\]