Question

34.A body slides down a rough inclined plane of angle of inclination 30degrees and takes time twice as great as the time taken in slipping down an identical frictionless plane.The coeffeicient of friction between the body and the plane is

Answer 1

$$\begin{gathered} Accelerationwhensurfaceissmooth \\ {a}_1=g\sin \theta \\ whensurfaceisrough \\ {a}_2=g\sin \theta -\mu g\cos \theta \\ dis\tan cetarvelledbybothissame \\ s=0.5a_1{t_1}^2 \\ s=0.5a_2{t_2}^2 \\ \frac{a_1}{a_2}=\frac{{t_2}^2}{{t_1}^1}=4 \\ g\sin \theta =4g\sin \theta -4\mu g\cos \theta \\ 4\mu g\cos \theta =3g\sin \theta \\ 4\mu \frac{\sqrt{3}}{2}=3\frac{1}{2} \\ \mu =\frac{\sqrt{3}}{4} \end{gathered}$$