Two masses of $5 \ kg$ and $10 \ kg$ are suspended from a massless pulley as shown in the figure. Calculate the acceleration of the system when the masses are left free.

An arrangement of a spring,strings,a pulley,and masses is shown in the figure below. The pulley and the strings are massless and $M > m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached,then immediately after detachment,

Two blocks of masses $1\,kg$ and $5\,kg$ are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a spring balance as shown in the figure. The blocks start moving; during this interval,the reading of the spring balance will be:

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:

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is