One end of a massless rope,which passes over a massless and frictionless pulley $P$,is tied to a hook while the other is free. The maximum tension the rope can bear is $360 \ N$. With what value of maximum safe acceleration (in $m \ s^{-2}$) can a man of $60 \ kg$ climb on the rope?

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 $\,N$)

$A$ lift of mass $1000\,kg$ is moving with an acceleration of $1\,m/s^2$ in the upward direction. The tension developed in the cable connected to the lift is ........... $N$ $(g = 9.8\,m/s^2)$.

Two blocks $A$ and $B$,each of the same mass,are attached by a thin inextensible string through an ideal pulley. Initially,block $B$ is held in position as shown in the figure. Now,block $B$ is released. Block $A$ will slide to the right and hit the pulley in time $t_A$. Block $B$ will swing and hit the surface in time $t_B$. Assume the surface is frictionless. [Hint: Tension $T$ in the string acting on both blocks is the same in magnitude. Acceleration needed for horizontal motion is provided by $T$.]

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2m$,then the stress produced in the wire is

Two bodies of mass $6 \ kg$ and $4 \ kg$ are tied to a string as shown in the adjoining figure. If the table and pulley are frictionless,then the acceleration of the $6 \ kg$ mass will be $........ \ ms^{-2}$ $\left(g=10 \ ms^{-2}\right)$.