Which of the following graph may represent the speed of block as a function of distance $s$ from the wall $w$ , when an iron block of mass $m$ resting in contact with a support $S$ is released when it has compressed the ideal spring on a smooth horizontal floor as shown. The block is not attached with the support $S$.

Potential energy function along $x-$axis, in a certain force field, is given as $U\left(x\right)=\frac{x^4}{4}-2x^3+\frac{11}{2}{x}^3-6x$. For the given force field,

$\left(\mathrm{i}\right)$ the points of equilibrium are $x=1, x=2$ and $x=3$.

$\left(\mathrm{ii}\right)$ the point $x=2$ is a point of unstable equilibrium.

$\left(\mathrm{iii}\right)$ the points $x=1$ and $x=3$ are points of stable equilibrium.

$\left(\mathrm{iv}\right)$ there exists no point of neutral equilibrium.

Which of the above statements is correct?

A block of $1 \mathrm{kg}$is placed at $A$of a rough track as shown in the figure. If slightly pushed towards the right, it stops at point $B$ of the track. The work done by the frictional force is $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A block of mass $\mathrm{m}=2 \mathrm{kg}$ is moving with velocity $v_0$ towards a massless unstretched spring of force constant $k=10 \mathrm{N} {\mathrm{m}}^{-1}$. The coefficient of friction between the block and the ground is, $\mu =\frac{1}{5}$. Find the maximum value of $v_0$ so that after pressing the spring, the block does not return back but stops there permanently.

A block of mass $m$ is placed inside a smooth hollow cylinder of radius $R$ whose axis is kept horizontally. Initially, the system was at rest. Now cylinder is given constant acceleration $2\mathit{ }g$ in the horizontal direction by an external agent. The maximum angular displacement of the block with the vertical is: 

A $10 \mathrm{kg}$ small block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius $10 \mathrm{m}$. The applied force is of $200 \mathrm{N}$ as shown in the figure. If the block started from rest at $A$, the speed at $B$ would be: $(g = 10 \mathrm{m} {\mathrm{s}}^{-2})$