A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is µ and tan θ > µ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg (sin θ – µ cos θ) to P2 = mg(sin θ + µ cos ), the frictional force f versus P graph will look like

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Tanθµ

force for which f = 0 P0 = mg sin
Case I P = mg (sin – µ cos ) P < P0

P + f = mg sin
mg (sinq – µcos) + f = mg sin
f = µ mgcos
Case II P = mg (sin + µ cos) > P0

P = f + mg sinq
mg (sinq + µ cos) = f + mg sin
f = µ mg cos]