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Q.

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 θμ cos θ ) to P2=mg(sin θ+μ cos θ), the frictional force  f versus P graph will look like

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a

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b

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c

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d

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answer is A.

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Detailed Solution

As tan θ>μ, the block has a tendency to move down the incline. Therefore a force P is applied upwards along the incline. Here, at equilibrium P+f=mg sinθ

f=mg sinθ-P

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Now as P increases, f decreases linearly with respect to P.
When P=mg sin θ, f=0.
When P is increased further, the block has a tendency to move upwards along the incline.
Therefore the frictional force acts downwards along the incline.
Here, at equilibrium P=f+mg sin θ
f=Pmg sin θ
Now as P increases, f increases linearly w.r.t P.
This is represented by graph (a)

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