Two springs with spring constants $K_1 = 1500 \, N/m$ and $K_2 = 3000 \, N/m$ are stretched by the same force. The ratio of potential energy stored in the springs will be

$A$ spring of $5 \times 10^3 \text{ Nm}^{-1}$ spring constant is stretched initially by $10 \text{ cm}$ from its unstretched position. The work required to stretch it further by another $10 \text{ cm}$ is: (in $\text{ J}$)

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

$A$ massless platform is kept on a light elastic spring as shown in the figure. When a sand particle of mass $0.1 \; kg$ is dropped on the pan from a height of $0.24 \; m$,the particle strikes the pan and the spring is compressed by $0.01 \; m$. From what height should the particle be dropped to cause a compression of $0.04 \; m$ (in $; m$)?

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 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 will be $.......\,U$.