See the figure given below. $A$ mass of $6 \; kg$ is suspended by a rope of length $2 \; m$ from the ceiling. $A$ force of $50 \; N$ in the horizontal direction is applied at the midpoint $P$ of the rope,as shown. What is the angle the rope makes with the vertical in equilibrium (in $^{\circ}$)? (Take $g = 10 \; m s^{-2}$). Neglect the mass of the rope.

As shown in the figure,the two sides of a step ladder $BA$ and $CA$ are $1.6 \; m$ long and hinged at $A$. $A$ rope $DE$ of length $0.5 \; m$ is tied halfway up. $A$ weight of $40 \; kg$ is suspended from a point $F$,$1.2 \; m$ from $B$ along the ladder $BA$. Assuming the floor to be frictionless and neglecting the weight of the ladder,find the tension in the rope and the forces exerted by the floor on the ladder. (Take $g = 9.8 \; m/s^2$)

Two equal heavy spheres,each of radius $r$,are in equilibrium within a smooth cup of radius $3r$. The ratio of the reaction between the cup and one sphere to that between the two spheres is:

$A$ $1 \text{ N}$ pendulum bob is held at an angle $\theta$ from the vertical by a $2 \text{ N}$ horizontal force $F$ as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is

$A$ body of mass $40 \,g$ is moving with a constant velocity of $2 \,cm/s$ on a horizontal frictionless table. The force on the table is ....... $dyne$.

$A$ flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^{\circ}$. Considering the equilibrium of each half of the chain,the tension of the chain at the lowest point is . . . . . . .