$A$ $100 \ N$ weight is suspended in a corner of a room by two cords $A$ and $B$ as shown in the figure. The tension in the horizontal cord $A$ is ............ $N$.

The adjoining figure shows a force of $40\, N$ acting at $30^o$ to the horizontal on a body of mass $5\, kg$ resting on a smooth horizontal surface. Assuming that the acceleration due to gravity is $10\, ms^{-2}$,which of the following statements is (are) correct?
$[1]$ The horizontal component of the applied force is $20\sqrt{3}\, N$.
$[2]$ The weight of the $5\, kg$ mass acts vertically downwards.
$[3]$ The net vertical force acting on the body is $30\, N$ (upwards).

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$-direction,the magnitude of the minimum additional force needed is:

The adjacent figure shows a part of a horizontally stretched net. Section $AB$ is stretched with a force of $10 \,N$. The tensions in the sections $BC$ and $BF$ are

When an object is at rest,

$A$ body is moving under the action of two forces $\vec{F}_1 = 2\hat{i} - 5\hat{j}$ and $\vec{F}_2 = 3\hat{i} - 4\hat{j}$. Its velocity will become uniform under an additional third force $\vec{F}_3$ given by: