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.

Two spherical objects each of radii $R$ and masses $m_1$ and $m_2$ are suspended using two strings of equal length $L$ as shown in the figure $(R << L)$. The angle $\theta$ which mass $m_2$ makes with the vertical is approximately

$A$ 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 $g = 10 \, ms^{-2}$)

$A$ box of mass $m$ is in equilibrium under the application of three forces as shown below. If the magnitude of $F_1$ is $10 \ N$, what is the magnitude of $F_3$ (in $N$)?

$A$ particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (assuming the particle is initially at rest):
$\vec{F}_1 = 5\hat{i} - 5\hat{j} + 5\hat{k}$
$\vec{F}_2 = 2\hat{i} + 8\hat{j} + 6\hat{k}$
$\vec{F}_3 = -6\hat{i} + 4\hat{j} - 7\hat{k}$
$\vec{F}_4 = -\hat{i} - 3\hat{j} - 2\hat{k}$
Then the particle will move:

$A$ metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong?