What is the minimum value of acceleration of wedge 80 that block start sliding? Given coefficient of friction between block and wedge is μ.

The free body diagram of the block isThe acceleration of the block is in the right direction so the block will experience a pseudo force in the left direction as shown in the free body diagram.The block will start sliding on the wedge then friction force will act down the wedge.The condition when block will slide on the wedge ismacos⁡θ⩾mgsin⁡θ+μNFor minimum accelerationmacos⁡θ=mgsin⁡θ+μN……….(1)Now resolving the components of different forces acting on the blockN=mgcos⁡θ+masin⁡θ………(2)macos⁡θ=mgsin⁡θ+μN………(3)On solving the equations (2) and (4)⇒a(cos⁡θ−μsin⁡θ)=g(sin⁡θ+μcos⁡θ)⇒a=g(sin⁡θ+μcos⁡θ)(cos⁡θ−μsin⁡θ)