$A$ weight $W$ can be hung in any of the following four ways by a string of the same type. In which case is the string most likely to break?

$A$ loop of light inextensible string passes over smooth small pulleys $A$ and $B$. Two masses $m$ and $M$ are attached to the points $O$ and $C$ respectively. The condition that $m$ and $M$ will cross each other (given $AB = 2l$ and $AC = BC = \eta l$) is:

Two weights of mass $m_{1}$ and $m_{2} (> m_{1})$ are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

To paint the side of a building,a painter normally hoists himself up by pulling on the rope $A$ as shown in the figure. The painter and platform together weigh $200 \, N$. The rope $B$ can withstand a maximum tension of $300 \, N$. Then:

The tension in the string connected between the two blocks is ......... $N$.

The pulley arrangements shown in the figure are identical, and the mass of the rope is negligible. In case $I$, the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In case $II$, the mass $m$ is lifted by pulling the other end of the rope with a constant downward force $F = 2mg$, where $g$ is the acceleration due to gravity. The acceleration of mass $m$ in case $I$ is