A body of mass m is placed on a rough surface with coefficient of friction μ inclined at θ. If the mass is in equilibrium, then

Consider a body of mass m placed on a rough inclined surface and it is just on the point of sliding down, with coefficient of friction μ inclined at angle θ, as shown in figure.At the equilibrium point O,In case of limiting condition, F = mg sin θ       …….(i)Normal force, R = mg cos θ            …….(ii)On dividing Eq. (i) by Eq. (ii), we getFR  = mg sinθmg cosθμ = tanθ                      (∵ Force of friction, F = μR)⇒  θ  = tan-1(μ)This is maximum value of θ for mass m to be at rest.For smaller θ, body will be at rest, i.e. in equilibrium.So, angle of repose, i.e. θ  = tan-1μ