The potential energy of a long spring when stretched by $2 \ cm$ is $U$. If the spring is stretched by $8 \ cm$,the potential energy stored in it is:

Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$,such that $K_P > K_Q$. They are stretched first by the same amount (case $a$),then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as,in case $(a)$ and case $(b)$ respectively:

The potential energy of a certain spring when stretched through a distance $S$ is $10 \, J$. The amount of work (in $J$) that must be done on this spring to stretch it through an additional distance $S$ will be

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the work done by the spring force is

$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?