The limiting friction between two bodies in contact is independent of

If a ladder weighing $250\,N$ is placed against a smooth vertical wall and the coefficient of friction between the ladder and the floor is $0.3$,what is the maximum force of friction available at the point of contact between the ladder and the floor?

As shown in the figure,a block of mass $\sqrt{3} \text{ kg}$ is kept on a horizontal rough surface with a coefficient of friction $\mu = \frac{1}{3 \sqrt{3}}$. $A$ force $F$ is applied on the vertical face of the block at an angle of $60^{\circ}$ with the horizontal. The minimum force $F$ required to just move the block is $3x$. Find the value of $3x$.
$\left[ g = 10 \text{ m/s}^2; \sin 60^{\circ} = \frac{\sqrt{3}}{2}; \cos 60^{\circ} = \frac{1}{2} \right]$

$A$ block of $1\, kg$ is stopped against a wall by applying a force $F$ perpendicular to the wall. If $\mu = 0.2$,then the minimum value of $F$ will be ....... $N$.

$A$ block of mass $M$ is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu$ and the acceleration due to gravity is $g$,calculate the minimum force required to be applied by the finger to hold the block against the wall.

If the normal force is doubled,the coefficient of friction is