(b) mg/cosθ
Explanation:
When the plane is accelerated to balance the block, a horizontal force F acts on the block such that its component along the plane Fcosθ is equal and opposite to component of the weight along the plane mg.sinθ, see the figure on the right. So, Fcosθ = mg.sinθ → F= mg.tanθ. The components of F and weight mg perpendicular to plane (Fsinθ and mgcosθ) together push the plane. Equal and opposite force is exerted by the plane on the block as per "Newton'* Third Law of Motion" and its value is = Fsinθ + mgcosθ
= mg.tanθ.sinθ + mgcosθ =mg(sin2θ +cos2θ)/cosθ = mg/cosθ
