question_answer

A body takes time't' to reach the bottom of an inclined plane of angle \[\theta \] with the horizontal. If the plane is made rough, time taken new is 2t. The coefficient of friction of the rough surface is:

A) \[\frac{3\tan \,\theta }{4}\]                     

B) \[\frac{2\tan \,\theta }{3}\]

C) \[\frac{\tan \,\theta }{4}\]                       

D) \[\frac{\tan \,\theta }{2}\]           

Correct Answer: A

Solution :

[a] \[a=g\,Sin\,\theta \] \[{{S}_{1}}=\frac{1}{2}g\,Sin\,\theta {{t}^{2}}\] \[{{S}_{2}}=\frac{1}{2}g\,[Sin\,\theta -\mu \,Cos\theta ]\,(2{{t}^{2}})\] \[\frac{1}{2}g\,Sin\,\theta {{t}^{2}}=\frac{1}{2}g\,[Sin\,\theta -\mu Cos\theta ]\,4{{t}^{2}}\] \[Sin\,\theta =4\,Sin\,\theta -4\mu \,Cos\theta \] \[4\mu \,Cos\theta =3\,Sin\theta \] \[\mu \,=\frac{3}{4}\tan \theta \]