A ladder of length 5 m is placed against a smooth wall as shown in figure. The coefficient of friction is…..

Q: A ladder of length 5 m is placed against a smooth wall as shown in figure. The coefficient of friction is μ between ladder and ground. What is the minimum value of  μ , if the ladder is not to slip ?

(a) μ = 1/2

(b) μ = 1/4

(c) μ = 3/8

(d) μ = 5/8

Ans: (c)

Solution: Let normal reaction at B is N₁  & at A is N₂  

For Translational Equilibrium

N₁ = mg

f = N₂

μ N₁ = N₂

μ mg = N₂

μ = N₂/mg —(i)

For rotational Equilibrium
N₂ × OA = (mg)(2.5 cosθ)

Since, cosθ = 3/5 (from figure)

N₂ × 4 = 3mg/2

N₂/mg = 3/8

μ = 3/8 from(i)