Assertion: When a spring is elongated work done by spring is negative but when it compressed work done by spring is positive.

Reason: Work done by spring is path independent.

The graphs below show the magnitude of the force on a particle as it moves along the positive $X$-axis from the origin to $X=X_1$. The force is parallel to the $X$-axis and conservative. The maximum magnitude $F_1$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

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