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 ..........  $N$ $(g = 10\,ms^{-2})$ 

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ the net force on the particle (directed towards the centre) is :

$(i) \;T,$ $(ii)\; T-\frac{m v^{2}}{l},$ $(iii)\;T+\frac{m v^{2}}{l},$ $(iv) \;0$

$T$ is the tension in the string. [Choose the correct alternative].

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 

Which of the following sets of concurrent forces may be in equilibrium

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

A uniform rope of mass $M$ and length $L$ is fixed at its upper end vertically from a rigid support. Then the tension in the rope at the distance $l$ from the rigid support is $x$