For the given system,the acceleration of the system is ........... $m/s^2$.

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.

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is ($T$ is the tension in the string).

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly,then

In the system shown in the figure,the acceleration of the $1\,kg$ mass and the tension in the string connecting between $A$ and $B$ is

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 $g = 10\, ms^{-2}$)