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

Two plates each of mass $m$ are connected by a massless spring as shown below. $A$ weight $W$ is placed on the upper plate which compresses the spring further. When $W$ is removed,the entire assembly jumps up. The minimum weight $W$ needed for the assembly to jump up when the weight is removed is just more than ...........$m$.

$A$ spring whose unstretched length is $\ell$ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants $k_1$ and $k_2$ will be:

$A$ spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel,the force constant of the combination will be

The tension in the spring is ............ $N$.

$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of