Write the dimensional formula of $\frac {k}{m}$.

$A$ 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

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k.$ The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.

Statement $-1$: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$

Statement $-2$ : $k_1 < k_2$.

A block  $'A'$  of mass $M$ moving with speed $u$ collides elastically with block $B$ of mass $m$ which is connected to block $C$ of mass $m$ with a spring. When the compression in spring is maximum the velocity of block $C$ with respect to block $A$ is (neglect friction)

A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d.$ The net work done in the process is