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

Two masses $m_1 = 2\,kg$ and $m_2 = 5\,kg$ are moving on a frictionless surface with velocities $10\,m/s$ and $3\,m/s$ respectively. An ideal spring with spring constant $K = 1120\,N/m$ is attached to the back of $m_2$. The maximum compression of the spring will be ............... $m$.

$A$ $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N/m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $m/s$ $(g = 10\, m/s^2)$.

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:

$A$ mass of $1 \ kg$ falls from a height of $1 \ m$ and lands on a massless platform supported by a spring having spring constant $15 \ N \ m^{-1}$ as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity $= 10 \ m \ s^{-2}$)

The potential energy of a weightless spring compressed by a distance $a$ is proportional to