$A$ mass '$M$' is suspended by a rope from a rigid support at point '$P$' as shown in the figure. Another rope is tied at end '$Q$' and pulled horizontally with a force '$F$'. If the rope makes an angle '$\theta$' with the vertical,then the tension in the string '$PQ$' is

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 $\sqrt{2}$)

$A$ block is being pulled by a force $F$ on a long frictionless level floor. The magnitude of the force is gradually increased from zero until the block lifts off the floor. Immediately after the block leaves the floor,its acceleration is

$A$ $1 \,kg$ mass is suspended from the ceiling by a rope. $A$ horizontal force $F$ is applied at the midpoint of the rope so that the upper part of the rope makes an angle of $45^{\circ}$ with respect to the vertical axis as shown in the figure. The magnitude of $F$ is:

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

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.