Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A $15\, kg$ weight is attached to the rope at the mid-point, which now no longer remains horizontal. The minimum tension required to completely straighten the rope is

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 ................

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

Two equal heavy spheres, each of radius $r$, are in equilibrium within a smooth cup of radius $3 r$. The ratio of reaction between the cup and one sphere and that between the two sphere is

A car accelerates on a horizontal road due to the forces exerted by

A book is lying on the table. What is the angle between the action of the book on the table and the reaction of the table on the book?

When a body is stationary