Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.

$A$ uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ hanging on one side and the rest of its length $L - l$ hanging on the other side of the pulley. At a certain point in time,when $l = \frac{L}{x}$,the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........

$A$ uniform rope of mass $M$ and length $L$ is fixed at its upper end vertically from a rigid support. The tension in the rope at a distance $l$ from the rigid support is:

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).

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

Tension in the rope at the rigid support is ............ $N$ $\left(g=10 \,m / s ^2\right)$