$A$ light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$,then the ratio of the masses $\frac{m_2}{m_1}$ is:

Objects $A$ and $B$,each of mass $m$,are connected by a light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in the figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be

$A$ pulley fixed to the ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of the string and pulley are negligible. When the system is released,what is the acceleration of its centre of mass?

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 ($T$ is the tension in the string).

Both the blocks shown in the figure have mass $m$ and are moving with constant velocity in the directions indicated. They are in a resistive medium which exerts an equal constant force $F$ on both blocks in the direction opposite to their velocity. The tension in the string connecting them is: (Neglect friction)

Two blocks $A$ and $B$, each of mass $20 \,kg$, lying on a frictionless table, are connected by a light string. The system is pulled horizontally with an acceleration of $2 \,ms^{-2}$ by a force $F$ applied on block $B$. The tension in the string will be: (in $\,N$)