$A$ body of mass $1 \ kg$ is suspended with the help of two strings making angles as shown in the figure. The magnitudes of tensions $T_1$ and $T_2$,respectively,are (in $N$):

$A$ mass of $10\,kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point,the rope deviates at an angle of $45^o$ from the vertical. If the suspended mass is at equilibrium,the magnitude of the force applied is .......... $N$ $(g = 10\,ms^{-2})$.

Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium,then

If the tension in the horizontal wire shown in the figure is $30 \text{ N}$,then the weight $W$ and tension in the wire $OA$ are respectively:

$A$ man is standing on a balance and his weight is measured. If he takes a step to the left side,then his weight:

$A$ mass of $10 \, kg$ is suspended vertically by a rope of length $5 \, m$ from the roof. $A$ force of $30 \, N$ is applied at the middle point of the rope in the horizontal direction. The angle made by the upper half of the rope with the vertical is $\theta = \tan^{-1}(x \times 10^{-1})$. The value of $x$ is ................
(Given $g = 10 \, m/s^2$)