If the coefficient of friction between the wedge A and block B shown in the figure is μ , then the maximum possible horizontal acceleration of A for which B doesn't slip is [angle of inclination of wedge = 45 ° ]

Step-by-step solution

FBD of block B w.r.t. wedge A , for maximum ' a ' : Perpendicular to wedge: Σf y = ( mgcosθ + masinθ - N ) = 0 and Σ f x = mgsin θ + μ N - macos θ = 0 (for maximum a) ⇒ mgsinθ + μ ( mgcosθ + masinθ ) - macosθ = 0 ⇒ a = ( gsinθ + μgcosθ ) cosθ - μsinθ for θ = 45 ° a = g tan 45 ° + μ cot 45 ° - μ ; a = g 1 + μ 1 - μ