See Figure given below.  A mass of $6 \;kg$ is suspended by a rope of length $2 \;m$ from the ceiling. A force of $50\; N$ in the horizontal direction is applied at the midpoint $P$ of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take $g = 10 \;m s^{-2}$). Neglect the mass of the rope.

A man is pulling on a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points

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

Three forces starts acting simultaneously on a particle moving with velocity $\vec v.$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ (as shown). The particle will now move with velocity

There are three forces $\vec {F_1}$, $\vec {F_2}$ and $\vec {F_3}$ acting on a body, all acting on a point $P$ on the body. The body is found to move with uniform speed.

$(a)$ Show that the forces are coplanar.

$(b)$ Show that the torque acting on the body about any point due to these three forces is zero.