Question

a block kept on a rough inclined plane as shown in the figure , remains at rest upto a maximum force of 2newton down the inclined plane. max external force that doesnt move the block up is 10 newton, Coefficient of static friction
between block and plane

Answer 1

Answer :- √3/2

With condition of equilibrium.

$R+P sin \alpha=W cos \lambdaF= P cos \alpha + W sin \lambdaUse  F=\mu RP = W sin ( Θ - \lambda)/ cos ( \alpha - Θ)\\\\P = Pulling force \alpha= Angle of P \\\lambda= Inclined angleR = ReactionW = Weight\\\\For 2N force2+mg \sin \theta = \mu mg\cos 30 ........(1)For 10N force10= mg\sin 30+\mu mg\cos 30 ........(2)From (1) and (2)12 = 2\mu mg \cos \left ( 30 \right )8=mg\sin 30\\\mu = \sqrt{3}/2$