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.

$A$ $4 \text{ kg}$ mass is suspended as shown in the figure. All pulleys are frictionless and the spring constant $K$ is $8 \times 10^3 \text{ Nm}^{-1}$. The extension in the spring is $\left(g=10 \text{ ms}^{-2}\right)$.

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

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

Two masses $m_1 = 10 \ kg$ and $m_2 = 6 \ kg$ are attached to a string which passes over a frictionless smooth pulley. The acceleration of the masses is .......... $m/s^2$. (Take $g = 10 \ m/s^2$)

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is: