A 34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F f and F w are the reaction forces of the floor and the wall, then ratio of F w F f will be : (Use g = 10 m s - 2 .)

Step-by-step solution

Applying force balance in vertical direction N 1 = m g = 100   N Applying torque balance at the bottom contact point, m g × 3 2 = N 2 × 5 ⇒ N 2 = F w = 30   N Applying force balance in horizontal direction f s = N 2 = 30   N Net reaction at the floor will be, F f = N 1 2 + f s 2 = 100 2 + 30 2 = 10 109   N Therefore, F w F f = 30 10 109 = 3 109