$A$ light spring of length $20 \ cm$ and force constant $2 \ kg/cm$ is placed vertically on a table. $A$ small block of mass $1 \ kg$ falls on it. The height $h$ from the surface of the table at which the block will have the maximum velocity is ............... $cm$.

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

$A$ 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

Two identical springs have the same force constant $73.5 \,Nm^{-1}$. The elongation produced in each spring in the three cases shown in Figure-$1$,Figure-$2$,and Figure-$3$ are (given $g=9.8 \,ms^{-2}$):

$A$ massless spring gets elongated by an amount $x_1$ under a tension of $5 \ N$. Its elongation is $x_2$ under a tension of $7 \ N$. For an elongation of $(5x_1 - 2x_2)$,the tension in the spring will be: (in $N$)

$A$ bead of mass $m = 100 \,g$ is attached to one end of a spring of natural length $L$ and spring constant $k = \frac{(\sqrt{3}+1) mg}{L}$. The other end of the spring is fixed at point $A$ on a smooth vertical ring of radius $R$. The bead is at point $B$ such that the spring makes an angle of $30^{\circ}$ with the horizontal diameter. The normal reaction at $B$ just after it is released to move is (take $g = 9.8 \,ms^{-2}$): (in $\,N$)