Define spring constant and write its unit.

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block To an observer

$A$, the work done by the normal reaction $N$ between the block and the spring on the block is

Two blocks $A$ and $B$ of mass $m$ and $2\, m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. Spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is :-

A block of mass $m = 0.1\,kg$ is connected to a spring of unknown spring constant $k.$ It is compressed to a distance $x$ from its equilibrium. position and released from rest . After approaching half the distance $(\frac {x}{2})$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3\,ms^{-1}.$ The total initial energy of the spring is ................ $\mathrm{J}$

In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be

Two springs of spring constants $1500\, N/m$ and $3000\, N/m$ respectively are stretched with the same force. They will have potential energy in the ratio