An elevator accelerates upwards at a constant rate. $A$ uniform string of length $L$ and mass $m$ supports a small block of mass $M$ that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$. The acceleration of the elevator is

$A$ system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system is in equilibrium, then the value of $m$ is (in $\,kg$)

Two blocks of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg$. The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$.

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is

$A$ body of mass $M$ tied to a string is lowered at a constant acceleration of $(g/4)$ through a vertical distance $h$. The work done by the string will be..............