Two objects $A$ and $B$ each of mass $m$ are connected by a light inextensible string. They are restricted to move on a frictionless ring of radius $R$ in a vertical plane (as shown in fig). The objects are released from rest at the position shown. Then, the tension in the cord just after release is

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface., the acceleration of mass $m$ is

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 $B.$

As shown in figure, a $70\,kg$ garden roller is pushed with a force of $\overrightarrow{ F }=200\,N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is $.......\,N$ $\left(\right.$ Given $\left.g =10\,m s ^{-2}\right)$

A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_1$ and $F_2 (< F_1 )$ as shown in the following figure.The tension in the rod at a distance $y$ from the end $A$ is given by

The ends of a rope are held by two men who pulls on it with equal and opposite forces of  magnitude $F$ each. Then the tension in the rope is