In the arrangement shown in the figure,the pulley is smooth and massless,and all the strings are light. Let $F_1$ be the force exerted on the pulley in case $(i)$ and $F_2$ be the force in case $(ii)$. Then:

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \ kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \ N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \ m/s^2$).

The ideal mechanical advantage of the combination of pulleys shown is

In the adjoining figure,the tension in the string connecting blocks $A$ and $B$ is:

In order to raise a mass of $100\,kg$,a man of mass $60\,kg$ fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $5g/4$ relative to the rope. The tension in the rope is ....... $N$. $(g = 10\,m/s^2)$

Two masses $M$ and $M/2$ are joined together by means of a light inextensible string passing over a frictionless pulley as shown in the figure. When the bigger mass is released,the smaller one will ascend with an acceleration of