A rectangular wall 4 meters high and 5 meters wide is to be painted. If the cost of painting the entire wall is Rs. 15 per square meter, what will be the total cost?

Step 1: Identify forces acting on the ladder. The ladder has weight W = 200\ N acting downward at its center. Normal reaction N_g from ground upward at lower end A. Friction f ≤ N_g at A, toward the wall ( = 0.4). Normal reaction N_w from wall, horizontal away from wall, at upper end B. Ladder length L = 5\ m. cancel Step 2: Resolve vertically at A. N_g = W N_g = 200\ N Step 3: Resolve horizontally. f = N_w For no slipping at minimum , f = N_g. N_g = N_w N_w = 0.4 × 200\ N = 80\ N Step 4: Take moments about A (eliminates N_g and f). Clockwise moment by weight: W × (L)/(2) . Anticlockwise moment by N_w: N_w × L . For equilibrium: N_w L = W (L)/(2) Cancel L: N_w = W (1)/(2) = (W)/(2 N_w) Substitute W = 200\ N, N_w = 80\ N: = (200)/(2 × 80) = (200)/(160) = 1.25 = 1.25 = ^-1(1.25) Step 5: Calculate numerical value. 1.25 = (5)/(4) = ^-1((5)/(4)) ≈ 51.34^ _min = ^-1(1.25) ≈ 51.3^ (or exactly _min = ^-1(2 × 0.4) = ^-1(0.8)) _ ≈ 51.3^