$A$ rope of mass $5 \,kg$ is hanging between two supports as shown. The tension at the lowest point of the rope is close to ........... $N$ (take $g=10 \,m/s^2$).

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces? Also,name the triangle formed by the forces as sides.

Statement-$I$: If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\vec{F}_{1} + \vec{F}_{2} = -\vec{F}_{3}$,then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement-$II$: $A$ triangle made up of three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ as its sides taken in the same order,satisfy the condition for translatory equilibrium.
In the light of the above statements,choose the most appropriate answer from the options given below:

Three concurrent co-planar forces $1 \,N$,$2 \,N$,and $3 \,N$ acting along different directions on a body:

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 $x = ....$

When is an object said to be in equilibrium?