What is the minimum coeffecient of static friction μmin required between the ladder and the ground so that the ladder does not slip?

Explanation:

let the ladder is of mass "m" and standing at an angle with the ground

So here by horizontal force balance we will have

by vertical force balance we have

now by torque balance about contact point on ground we will have

so we will have

now from first equation we have

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2