A body is in equilibrium when force  $F_1$ and $F_2$ are applied to it. The magnitude of the difference of forces is (Given that:$\left|F_1\right|=\left|F_2\right|$)

A rectangular frame of some mass has to be suspended symmetrically by two mass-less strings of equal length on two supports. It can be done in one of the three following ways as shown in below figures. The tension in the strings will be

A $90 \mathrm{N}$ mass is hung on a rope tied between two poles as shown in the figure. The tension $T_1$ and $T_2$ in the two parts of the rope are (in $\mathrm{N}$)

A particle moving with velocity $\overrightarrow{V}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will

A block of mass $200 \mathrm{g}$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F=\sqrt{x} \mathrm{N}$ as shown in figure.

The value of $x=\_\_\_\_\_$.

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

(Given, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1:x$, where $x=$_____ .

The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be:

For a free body diagram shown in the figure, the four forces are applied in the '$x$' and '$y$' directions. What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?

Three forces $F_1=10 \mathrm{N}, F_2=8 \mathrm{N}, F_3=6 \mathrm{N}$ are acting on a particle of mass $5 \mathrm{kg}$. The forces $F_2$ and $F_3$ are applied perpendicularly so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is

A block of $\sqrt{3} \mathrm{kg}$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30°$ with the wall. The tension $T$ is : (Given g $=10 \mathrm{m} {\mathrm{s}}^{–2}$)