An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

The work done in stretching a spring from $10 \ cm$ to $20 \ cm$ is:

$A$ spring of force constant $10\, N/m$ has an initial stretch $0.20\, m$. In changing the stretch to $0.25\, m$,the increase in potential energy is about.....$joule$.

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$,respectively,are stretched by the same force,it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement $1$: If stretched by the same amount,the work done on $S_1$ is more than on $S_2$.
Statement $2$: $k_1 < k_2$.

Two particles with mass $m_1 = 16 \ kg$ and $m_2 = 2 \ kg$ slide as a unit with a common velocity of $12 \ ms^{-1}$ on a level frictionless surface. Between them is a compressed massless spring with spring constant $k = 100 \ Nm^{-1}$. The spring,originally compressed by $25 \ cm$,is suddenly released,sending the two masses,which are connected to the spring,flying apart from each other. The orientation of the spring w.r.t. the initial velocity is shown in the diagram. What is the relative velocity of separation in $ms^{-1}$,after the particles lose contact?

The work done in joules in increasing the extension of a spring of stiffness $10\, N/cm$ from $4\, cm$ to $6\, cm$ is: