See 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 ? (Take $g = 10 \;m s^{-2}$). Neglect the mass of the rope.

For given systen $T_2$ ……. 

There are four forces acting at a point $P$ produced by strings as shown in figure. Which is at rest ? Find the forces $F_1$ and $F_2$.

A mass of $10 \,kg$ is suspended vertically by a rope of length $5 \,m$ from the roof. A force of $30 \,N$ is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta=\tan ^{-1}\left(x \times 10^{-1}\right)$. The value of $x$ is …………….

$\text { (Given } g =10 \,m / s ^{2} \text { ) }$