Determine the resultant force when three forces such as $80 \mathrm{N}, 100 \mathrm{N}$, and $30 \mathrm{N}$ are acting on an object simultaneously and $30 \mathrm{N}$ force is opposite to the other two forces.

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 $\mathrm{N}$)

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?

The sum of the three vectors in the figure below is zero. The magnitude of $\overrightarrow{\mathrm{OC}}$ and $\overrightarrow{\mathrm{OB}}$ 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 $=10 \mathrm{m} {\mathrm{s}}^{–2}$)

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:

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

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