Answer :

(a)For this condition to be true, the forces must balance each other.
The frictional force(f) is given by:



Therefore,





where, μ is the coefficient of friction, N is the normal to the surface, g is the acceleration due to gravity and θ is the angle of the incline.


So for θ equal to tan-1(μ), the box just starts to slide.


(b) From the figure, we can resolve the forces for 𝜶 > 𝜽:



(c)In this scenario, as we trying to move the box up the plane, the direction of friction changes and is now acting down the plane.


The equation of force is:



(d)Here, the acceleration is in the direction of the force. Thus resolving the forces, we have,



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