In the figure given below,with what acceleration will the block of mass $m$ move? (Pulley and strings are massless and frictionless)

In the given figure,two masses $m_1$ and $m_2$ $(m_2 > m_1)$ are at rest in an equilibrium position. Find the tension in string $AB$.

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$,the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$,the acceleration of the system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be:

Two bodies of mass $3\, kg$ and $4\, kg$ are suspended at the ends of a massless string passing over a frictionless pulley. The acceleration of the system is ........ $m/s^2$ $(g = 9.8\, m/s^2)$.

$A$ 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?

$A$ uniform rope of mass $M$ and length $L$ is fixed at its upper end vertically from a rigid support. The tension in the rope at a distance $l$ from the rigid support is: