The potential energy of a long spring when it is stretched by $3 \ cm$ is $U$. If the spring is stretched by $9 \ cm$,the potential energy stored in it will be: (in $U$)

Two massless springs of spring constants $K_1$ and $K_2$ are connected in series, suspended vertically, and a mass is attached to the free end. If $x_1$ and $x_2$ are their respective extensions and $F$ is the stretching force, what is the total extension produced?

Two springs $A$ and $B$ are fixed at the top and are stretched by $8 \,cm$ and $16 \,cm$ respectively, when loads of $20 \,N$ and $10 \,N$ are suspended at the lower ends. The ratio of the spring constants of the springs $A$ and $B$ is (in $: 1$)

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, $k$)

$A$ spring of force constant $k$ is cut into three equal parts. The force constant of each part would be

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 $A$.