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 rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta=\tan ^{-1}\left(x \times 10^{-1}\right)$. The value of $x$ is ................

$\text { (Given } g =10 \,m / s ^{2} \text { ) }$

A car of mass $m$ when passes over top of convex bridge of radius of curvature $r,$ with a velocity $v,$ then the normal force exerted by the bridge on the car is 

A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_1$ and $F_2 (< F_1 )$ as shown in the following figure.The tension in the rod at a distance $y$ from the end $A$ is given by

What are concurrent forces ? Explain equilibrium of particle under effect of concurrent forces.

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 deviated at an angle of $45^o$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ..........  $N$ $(g = 10\,ms^{-2})$ 

A weight $M g$ is suspended from the middle of a rope whose ends are at the same level. The rope is no longer horizontal. The minimum tension required to completely straighten the rope is ......