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

$A$ body of mass $m$ is allowed to fall with the help of a string with downward acceleration $\frac{g}{6}$ to a distance $x$. The work done by the string is .............

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. The whole system is moving upwards with an acceleration of $2\, ms^{-2}$. The tensions $T_1$ and $T_2$ are respectively (Take $g = 10\, ms^{-2}$)

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 uses two pulleys to raise himself with an acceleration of $2\,m/s^2$,as shown in the figure. The man stands on a light weighing machine fitted on a horizontal platform. Determine the reading of the weighing machine. (Mass of man $= 75\,kg$,mass of platform $= 25\,kg$,$g = 10\,m/s^2$) (in $,N$)

Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............