$A$ 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 ............... $cm$.

Fill in the blank: The force constant of a spring is $0.5 \, Nm^{-1}$. The force necessary to increase the length of the spring by $10 \, cm$ will be .......... (in $, N$)

$A$ block of mass $m$ is released suddenly from the top of a spring with a spring constant $k$. $(i)$ What will be the maximum compression in the spring? $(ii)$ What will be the compression in the spring at the equilibrium position?

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

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length,the line $OA$ will

Initially,a spring is at its natural length. $A$ block of mass $2 \, kg$ is attached to the lower end,and a block of mass $0.25 \, kg$ is at the top. If the system is released from the position where the spring is at its natural length,find the maximum force exerted by the system on the floor? (in $N$,take $g = 10 \, m/s^2$)