For the pulley system shown in the figure,calculate the kinetic energy of the $6\,kg$ block after $5\,s$. (Assume $g = 10\,m/s^2$)

The maximum acceleration with which a body of mass $200 \, kg$ is lowered into a well using a rope having a breaking force of $50 \, kg$-wt is (Acceleration due to gravity $= 10 \, ms^{-2}$) (in $ \, ms^{-2}$)

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 ....... $N$. $(g = 10\,m/s^2)$

$A$ particle of small mass $m$ is joined to a very heavy body of mass $M$ by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

$A$ 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:

$A$ 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.