The potential energy of a particle of mass $5\mathrm{ }\mathrm{k}\mathrm{g}$ moving in the $\mathrm{x}\mathrm{y}$ plane is given as

$\mathrm{U}=-\mathrm{ }7\mathrm{x}\mathrm{ }+\mathrm{ }24\mathrm{ }\mathrm{y}\mathrm{ }\mathrm{J}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}$, $\mathrm{x}$ and $\mathrm{y}$ in meters. Initially at $\mathrm{t}=0$ the particle is at the origin $\left(0,\mathrm{ }0\right)$ moving with a velocity of $\mathrm{v}=6\left[2.4\mathrm{ }\widehat{i}\mathrm{ }+\mathrm{ }0.7\mathrm{ }\widehat{j}\mathrm{ }\mathrm{m}/\mathrm{s}\right]$, then -

A particle is kept on the surface of a uniform sphere of mass $1000 \mathrm{kg}$ and radius $1 \mathrm{m}$. The work done per unit mass against the gravitational force between them is

In the figure, mass of $A$ is $m$ and that of $B$ is $2\mathrm{m}$. All the surface are smooth. System is released from rest with spring unstretched. Then, the maximum extension $X_m$ in spring will be

Two springs of force constants $k_1$ and $k_2$ are stretched by the same force. The ratio of potential energies stored in them is

Given below is the plot of a potential energy function $\mathrm{U}\left(\mathrm{x}\right)$ for a system, in which a particle is in one dimensional motion, while a conservative force $\mathrm{F}\left(\mathrm{x}\right)$ acts on it. Suppose that ${\mathrm{E}}_{\text{mech }}=8 \mathrm{J}$, the incorrect statement for this system is :

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 $\mathrm{k}=50 \mathrm{N} {\mathrm{m}}^{-1}$. The maximum compression of the spring would be

The figure shows the variation of potential energy with distance. The part of the graph which represents the repulsive force is