A block of mass m is placed on a smooth inclined wedge ABC of inclination $\mathrm{\theta }$ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and $\mathrm{\theta }$ for the block to remain stationary on the wedge is                                                        

 

detailed solution

Correct option is D

According to the question, the free body diagram of the given condition will beSince, the wedge is accelerating towards right with a, thus a pseudo force acts in the left direction in order to keep the block stationary. As, the system is in equilibrium.∴   ∑Fx = 0  or ∑Fy = 0⇒ R sinθ = ma                  .....(i)Similarly R cosθ = mg                  .....(ii)Dividing Eq. (i) by Eq (ii), we getR sinθR cosθ = mamg⇒ tanθ = ag or a = g tanθ∴  The relation between a and 9 for the block to remain stationary on the wedge is a = g tanθ.