A body of weight $2\, kg$ is suspended as shown in the figure. The tension ${T_1}$ in the horizontal string (in kg wt) is

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$ . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $'a'$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$ . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x$ , is

An object is subjected to a force in the north-east direction. To balance this force, a second force should be applied in the direction

The $50\,kg$ homogeneous smooth sphere rests on the $30^{\circ}$ incline $A$ and bears against the smooth vertical wall $B$. Calculate the contact forces at $A$ and $B.$

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.