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

$A$ spring with $10$ coils has spring constant $k$. It is exactly cut into two halves,then each of these new springs will have a spring constant

$A$ spring has length $l$ and force constant $K$. If it is cut into two springs of length $l_1$ and $l_2$ such that $l_1 = n l_2$ ($n$ is an integer). The force constant of the spring of length $l_2$ is

An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

The spring extends by $x$ on loading,then the energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is