Question

A block of mass m is placed on a inclined plane of inclination angle θ with horizontal. Coefficient of friction between block and plane is µ. tanθ > µ is kept. The block is kept stationary by applying force P parallel to plane. Direction of force P is taken positive in upward direction. When P is changed from P₁ = mg(sinθ - µ cosθ) to P₂ = mg(sinθ + µ cosθ), then the graph between force of friction f and P will represented by:

Answer 1

Correct option is : (a)

Limiting friction on the block,

f = µ.R = µmg cos θ

∴ P + f = mg sin θ

or f = mg sin θ - P

or µmg cos θ = mg sin θ - P

∴ P = (mg sin θ - µmg cos θ)

As force P changes from (mg sin θ - mg cos θ) to (mg sin θ + µmg cos θ), the value of f changes from µmg cos θ to -µm g cos θ.

Therefore graph (a) is correct.