Three masses of $1\, kg$,$6\, kg$,and $3\, kg$ are connected to each other with threads and are placed on a table as shown in the figure. The acceleration with which the system is moving is $....... \, ms^{-2}$. (Take $g = 10\, ms^{-2}$)

$A$ uniform chain of length $2L$ is hanging in an equilibrium position. If end $B$ is given a slightly downward displacement,the imbalance causes an acceleration. Here,the pulley is small and smooth,and the string is inextensible. Find the velocity $v$ of the chain when it slips out of the pulley (height of pulley from floor $> 2L$).

If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

$A$ pulley fixed to the ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of the string and pulley are negligible. When the system is released,what is the acceleration of its centre of mass?

The same spring is attached to $2 \ kg, 3 \ kg$ and $1 \ kg$ blocks in three different cases as shown in the figure. If $x_1, x_2$ and $x_3$ are the extensions in the spring in these cases,respectively,find the correct relation between them.

The tension in the string connected between the two blocks is ......... $N$.