A uniform ladder of length $5 \mathrm{m}$ is placed against the wall in vertical plane as shown in the figure. If coefficient of friction $\mathrm{\mu }$ is the same for both the wall and the floor then minimum value of $\mathrm{\mu }$ for it not to slip is 

A rod of weight $w$ is supported by two parallel knife edges$A \& B$and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at a distance $x$ from $A.$ The normal reactions at $A\text{ and} B$will be

The beam and pans of a balance have negligible mass. An object weighs $W_1$

when placed in one pan and $W_2$ when placed in the other pan. The weight W of the object is

A uniform rod of length $l$ is placed symmetrically on two walls as shown in figure. The rod is in equilibrium. If $N_1 \text{and} N_2$are the normal forces exerted by the walls on the rod then 

The uniform rod of mass$20 \mathrm{kg}$ and length $1.6 \mathrm{m}$ is pivoted at its end and swings freely in the vertical plane. Angular acceleration of rod just after the rod is released from rest in the horizontal position as shown in figure is