Find the acceleration of the $3 \text{ kg}$ mass when the acceleration of the $2 \text{ kg}$ mass is $2 \text{ ms}^{-2}$ as shown in the figure. (in $\text{ ms}^{-2}$)

Find the acceleration of $3\,kg$ mass when the acceleration of $2\,kg$ mass is $2\,ms^{-2}$ as shown in the figure.

The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it,its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them,then the extension will be

$A$ body of mass $m$ is suspended from an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

$A$ spring of force constant $15 \ N/m$ is cut into two pieces. If the ratio of their lengths is $1 : 3$, then the force constant of the smaller piece is . . . . . . $N/m$.