When a long spring is stretched by $2 \mathrm{cm}$, its potential energy is $\mathrm{U}$. If the spring is stretched by $10 \mathrm{cm}$, the potential energy stored in it will be

A mass of $0.5 \mathrm{kg}$ moving with a speed of $1.5 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal smooth surface collides with a nearly weightless spring of force constant $k=50 \mathrm{N} {\mathrm{m}}^{-1}$. The maximum compression of the spring would be:

A particle of mass $m$ oscillates in Simple Harmonic Motion between points $x_1$ and $x_2$, the equilibrium position being $O$. Which of the following graphs represents the variation of its potential energy $\left(U\right)$ with respect to its position?

A body performs SHM along the straight line segment $\mathrm{ABCDE}$ with $\mathrm{C}$ as the midpoint of segment $\mathrm{AE}$ ($\mathrm{A}$ and $\mathrm{E}$ are the extreme positions for the SHM). Its kinetic energies at $\mathrm{B}$ and $\mathrm{D}$ are each one fourth of its maximum value. If length of segment $\mathrm{AE}$ is $2\mathrm{R}$, then the distance between $\mathrm{B}$ and $\mathrm{D}$ is: