The ideal mechanical advantage of the combination of pulleys shown is

$A$ light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g / 8$,then the ratio of masses is

In the arrangement shown in the figure,the pulleys are massless and frictionless,and the threads are inextensible. The block of mass $m_1$ will remain at rest,if

$A$ $4 \text{ kg}$ 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 $\left(g=10 \text{ ms}^{-2}\right)$.

$A$ 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?

In the arrangement shown,the pulleys are fixed and ideal,the strings are light,$m_1 > m_2$ and $S$ is a spring balance which is itself massless. The reading of $S$ (in units of mass) is