The graph between kinetic energy $E$ and velocity $v$ is :

A block $\left(B\right)$ 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 $M2$ 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 on a particle of mass $m$ by a force $K\left[\frac{x}{{\left(x^2+y^2\right)}^{{\displaystyle \frac{3}{2}}}}\mathrm{i}+\frac{y}{{\left(x^2+y^2\right)}^{{\displaystyle \frac{3}{2}}}}\mathrm{j}\right]$ ($K$ being a constant of appropriate dimensions), when the particle is taken from the point $\left(a, 0\right)$ to the point $\left(0, a\right)$ along a circular path of radius $a$ about the origin in the $X-Y$ plane is:

A toy car of mass $5 \mathrm{kg}$ moves up a rampíunder the influence of force $F$ plotted against displacement $x.$ The maximum height attained is given by