When an object is at rest,

$A$ block of $\sqrt{3} \, kg$ 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 $30^{\circ}$ with the wall. The tension $T$ is $........... \, N$ : (Given $g = 10 \, ms^{-2}$)

$A$ rod $(AB)$ is attached to a fixed point $(C)$ using a light rope $(AC)$. The other end of the rod $(B)$ is resting on ice with negligible friction,and the system is in a stationary position. Which of the following can be the equilibrium configuration of this system?

$A$ 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:

$A$ flexible chain of weight $W$ hangs between two fixed points $A$ and $B$ which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is $\theta$. What is the tension of the chain at the mid point?

$A$ small sphere is hung by a string fixed to a wall as shown in the figure. The sphere is pushed from the wall by a stick. The forces acting on the sphere are as shown. Then,identify the incorrect expression.