Two masses $m_1$ and $m_2$ are connected by a light string passing over a smooth pulley. When set free,$m_1$ moves downwards by $3 \ m$ in $3 \ s$. The ratio of $\frac{m_1}{m_2}$ is $(g = 10 \ ms^{-2})$.

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

$A$ monkey of mass $40 \,kg$ climbs up a rope,of breaking load $600 \,N$ hanging from a ceiling. If it climbs up the rope with the maximum possible acceleration,then the time taken by the monkey to climb up is .........$s$ [Length of rope is $10 \,m$]

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:

For the system shown in the figure,the pulleys are light and frictionless. The tension in the string will be

Find the mechanical advantage for pulling mass $M$ by the person as shown in the figure.