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

Fill in the blank: $A$ spring is stretched by $3 \, cm$,its potential energy is $U_1$. If the spring is stretched by $6 \, cm$,its potential energy stored in it is $U_2 = ...... U_1$.

When equal forces are applied to two springs with spring constants $1500 \, N/m$ and $3000 \, N/m$,what is the ratio of their stored potential energies?

$A$ block $B$ is attached to two unstretched springs $S1$ and $S2$ with spring constants $k$ and $4k$,respectively (see figure $I$). The other ends are attached to identical supports $M1$ and $M2$ which are not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall $1$ by a small distance $x$ (figure $II$) and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is:

$A$ light elastic spring is placed on a massless platform as shown in the figure. $A$ sand particle of mass $0.1 \ kg$ is dropped onto the spring platform from a height of $0.24 \ m$. The particle sticks to the platform,causing the spring to compress by $0.01 \ m$. From what height should the particle be dropped so that the spring is compressed by $0.04 \ m$ (in $m$)?

$A$ mass of $1\, kg$ is hanging from a spring of spring constant $1\, N/m$. If Saroj pulls the mass down by $2\, m$,the work done by Saroj is......$J$.