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:

$A$ rope of length $5\,m$ is kept on a frictionless surface and a force of $5\,N$ is applied to one of its ends. Find the tension in the rope at $1\,m$ from this end.

Two identical blocks each of mass $M$ are attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. $A$ small mass $m$ is now placed on block $B$ (the right block). The acceleration with which the two blocks move together is ($g =$ gravitational acceleration).

Consider a situation in which both the horizontal and vertical surfaces of the block $M_0$ are smooth,as shown in the adjoining figure. $A$ force $F$ is applied to $M_0$. Mark the correct statement$(s)$.

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

$A$ painter is applying force himself to raise him and the box with an acceleration of $5\, m/s^2$ by a massless rope and pulley arrangement as shown in the figure. The mass of the painter is $100\, kg$ and that of the box is $50\, kg$. If $g = 10\, m/s^2$,then: