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 $: 1$)

When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

The spring extends by $x$ on loading,then the energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)

$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of

$A$ block of mass $2 \,kg$ is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end $A$ of the spring and speed of the block were measured to be $6 \,m/s$ and $3 \,m/s$, respectively. At this moment, the potential energy stored in the spring is increasing at a rate of $15 \,J/s$. Find the acceleration of the block at this instant. (in $\,m/s^2$)

$A$ spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel,the force constant of the combination will be