A block of mass $m=1\mathrm{kg}$ is placed on a plank of mass $M=2\mathrm{kg}$, which is placed on a horizontal frictionless surface. There is no friction between the block and the plank. Block and plank are connected by a spring of spring constant $6\mathrm{N} {\mathrm{m}}^{-1}$ as shown in the figure. An impulse $J=5\mathrm{N} \sec$ is applied on the plank. Possible magnitude of acceleration of the block during its subsequent motion is/are :

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 :

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