$A$ 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 ........

Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. The time taken for $m_1$ to reach the ground is ........ $\text{sec}$. (Assume the initial height is $0.2 \text{ m}$)

If the mass of block $B$ is $3\,kg$ and the mass of block $A$ is $7\,kg$,then the acceleration of the system is ........... $m/s^2$. $(g = 10\,m/s^2)$

In the adjoining figure,the tension in the string connecting blocks $A$ and $B$ is:

$A$ hanging mass $M$ is connected to a four times larger mass $(4M)$ by using a string-pulley arrangement as shown in the figure. The larger mass is placed on a horizontal ice slab and is being pulled by a $2Mg$ force. In this situation,the tension in the string is $\frac{x}{5}Mg$. Find the value of $x$. Neglect the mass of the string and the friction between the block (larger mass) and the ice slab. (Given $g$ = acceleration due to gravity)

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is