Two like parallel forces $20 \,N$ and $30 \,N$ act at the ends $A$ and $B$ of a rod $1.5 \,m$ long. The resultant of the forces will act at the point ........

A $\sqrt{34}\,m$ 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 $F _{ a } / F _{f}$ will be:

(Use $\left.g=10\,m / s ^{2}\right)$

$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $‘m’$ and side $‘a’$ which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between lines of action of $‘mg’$ and normal reaction $‘N’$ is :

A rod of mass $1\ kg$ , length $1\ m$ is suspended horizontally with the help of two ideal strings as shown in figure. First a mass is suspended to the left most end keeping rod horizontal, than a second mass is suspended to the right most end again keeping horizontal orientation. The maximum total mass that can be suspended in that way keeping horizontal orientation of rod ....... $kg.$

A heavy iron bar, of weight $\mathrm{W}$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is:

$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :