$A$ body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ respectively. If $T_1 = \sqrt{3} T_2$,then the angles $\theta_1$ and $\theta_2$ are:

Three forces $\vec{P}, \vec{Q},$ and $\vec{R}$ act at a point in a plane. The angles between $\vec{P}$ and $\vec{Q}$,and $\vec{Q}$ and $\vec{R}$ are $150^{\circ}$ and $120^{\circ}$ respectively. What is the ratio of the magnitudes of the forces $\vec{P}, \vec{Q},$ and $\vec{R}$ if the system is in equilibrium?

Write the condition for the translational equilibrium of a particle.

$A$ flexible chain of weight $W$ hangs between two fixed points $A$ and $B$ which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is $\theta$. What is the tension of the chain at the mid point?

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:

An iron sphere weighing $10 \, N$ rests in a $V$-shaped smooth trough whose sides form an angle of $60^o$ as shown in the figure. Then the reaction forces are: