When a weight is applied to a spring,it stretches by an amount $x$. What is the energy stored in it? ($T$ is the tension force developed in the spring and $k$ is the spring constant.)

$A$ spring has length $L$ and force constant $K$. It is cut into two springs of length $L_1$ and $L_2$ such that $L_1 = N L_2$ ($N$ is an integer). The force constant of the spring of length $L_1$ is:

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

To the free end of a spring hanging from a rigid support, a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is $d$. If the same block is attached to the same spring and allowed to fall suddenly, the amount of maximum stretching is: (force constant, $k$)

Two balls $A$ and $B$ of masses $100 \ gm$ and $250 \ gm$ are connected by a stretched massless spring and placed on a smooth table. When the balls are released simultaneously,the initial acceleration of ball $B$ is $10 \ cm/s^2$ towards the west. Find the magnitude and direction of the initial acceleration of ball $A$.

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