$A$ mass $M \text{ kg}$ is suspended by a weightless string. The horizontal force required to hold the mass at $60^{\circ}$ with the vertical is

$A$ 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 $N$)?

$A$ $1 \,kg$ mass is suspended from the ceiling by a rope. $A$ horizontal force $F$ is applied at the midpoint of the rope so that the upper part of the rope makes an angle of $45^{\circ}$ with respect to the vertical axis as shown in the figure. The magnitude of $F$ is:

$A$ 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?

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:

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.