$A$ 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 $g = 10 \ m/s^2$)

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 masses of $5\, kg$ and $10\, kg$ are connected to a pulley as shown. What will be the acceleration of the system if the pulley is set free? ($g =$ acceleration due to gravity)

Two masses $2 \, kg$ and $3 \, kg$ are attached to the ends of a string passed over a pulley fixed at the top. The tension and acceleration are:

If the tension in the cable of a $1000 \,kg$ elevator is $1000 \,kg$ weight,the elevator

$A$ mass of $10 \; kg$ is suspended by a rope of length $4 \; m$ from the ceiling. $A$ force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $F$ equals ........... $N$ (Take $g = 10 \; ms^{-2}$ and the rope to be massless).