Two weights $2 \,N$ and $3 \,N$ are suspended from the ends of an inextensible string passing over a fixed frictionless pulley. If the pulley is pulled up with an acceleration equal to the acceleration due to gravity $(g)$, then the tension in the string is: (in $\,N$)

$A$ $2 \, kg$ block is lying on a smooth table and is connected to a body of mass $1 \, kg$ by a string passing over a pulley. The $1 \, kg$ mass is hanging vertically. Find the acceleration of the block and the tension in the string.

The system of two masses $2 \ kg$ and $3 \ kg$ as shown in the figure is released from rest. The work done on the $3 \ kg$ block by the force of gravity during the first $2 \ s$ of its motion is $\left(g=10 \ m/s^2\right)$. (in $J$)

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:

$A$ man of mass $60 \ kg$ is standing on a platform of mass $40 \ kg$ as shown in the figure. What force should the man apply on the rope so that he accelerates upward with the platform with an acceleration of $2 \ m/s^2$ (in $N$)? (Take $g = 10 \ m/s^2$)

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be: