Block $A$ of mass $4 \; kg$ is to be kept at rest against a smooth vertical wall by applying a force $F$ as shown in the figure. The force required is .......... $N$ $\left(g = 10 \; m/s^2\right)$. (in $\sqrt{2}$)

$A$ uniform sphere of weight $W$ and radius $R = 3\,m$ is held by a string of length $L = 2\,m$ attached to a frictionless wall as shown in the figure. The tension in the string is:

Four forces are acting at a point $P$ in equilibrium as shown in the figure. The ratio of force $F_{1}$ to $F_{2}$ is $1: x$,where $x = ....$

What are concurrent forces? Explain the equilibrium of a particle under the effect of concurrent forces.

$A$ ladder rests against a frictionless vertical wall,with its upper end $6 \, m$ above the ground and the lower end $4 \, m$ away from the wall. The weight of the ladder is $500 \, N$ and its center of gravity ($C$.$G$.) is at $1/3$ of its length from the lower end. The reaction force from the wall will be (in Newton):

$A$ mass $M \text{ kg}$ is suspended by a weightless string. The horizontal force required to hold the mass at $60^{\circ}$ with the vertical is