In order to test the strength of a rope, one end is tied to a large tree and the other end is  hitched to a team of $2$ horses. The horse pull as hard as they can, but cannot break the  rope. If the rope is untied from the tree and attached to another team of $2$ horses  with equal strength, and the two teams pull in opposite directions, the tension in the rope  will

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 body of mass $60\,kg$ is suspended by means of three strings $P, Q$ and $R$ as shown in the figure is in equilibrium. The tension in the string $P$ is $..........g\,N$

A piece of wire is bent in the shape of a parabola $y=k x^2$ ( $y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $\alpha$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

Write different type of common forces.

A uniform sphere of weight $W$ and radius $5\, cm$ is being held by a string as shown in the figure. The tension in the string will be