$A$ ball of mass $m$ is dropped from a height $h$ on a platform fixed at the top of a vertical spring,as shown in the figure. The platform is depressed by a distance $x$. Then the spring constant is

The system of the wedge and the block connected by a massless spring as shown in the figure is released with the spring in its natural length. Friction is absent. The maximum elongation in the spring will be:

$A$ 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:

The work done in stretching a spring of natural length $25 \ cm$ and spring constant $50 \ Nm^{-1}$ from $50 \ cm$ to $60 \ cm$ is (in $J$)

When a spring is stretched by $2 \ cm$,it stores $100 \ J$ of energy. If it is stretched by another $2 \ cm$,the additional energy stored is ....... $J$.

If the potential energy of a spring is $V$ on stretching it by $2 \, cm$,then its potential energy when it is stretched by $10 \, cm$ will be