Conservative and Non-conservative Forces

The potential energy of a particle as function of position $x$ is given by$U=(x²-4x+2) \mathrm{J}$, where$x$ is in metre. The equilibrium position of the particle will be

A body of mass $1 \mathrm{kg}$ is suspended from massless spring of natural length $1 \mathrm{m}$. If mass is released from rest, spring can stretch up to a vertical distance of $40 \mathrm{cm}$, the potential energy stored in the spring at this extension is ($g= 10 \mathrm{m}/{\mathrm{s}}^2$)

When a spring is stretched by $2 \mathrm{cm}$, the energy stored is $100 \mathrm{J}$. If it is stretched further by $2 \mathrm{cm}$, its energy increases by _____.

Which of the following is non-conservative force?

A particle of mass $2 \mathrm{kg}$ has potential energy $U=\left(8x^2-4x^4\right) \mathrm{J}$. Then its angular frequency for small oscillation about its equilibrium position will be,

Which one of the following is not a conservative force?

Which of the following forces is not conservative?

The $\mathrm{P}.\mathrm{E}.$ of a particle of mass $0.1 \mathrm{kg}$ moving along the $x$- axis is given by, $U=5x\left(x-4\right) \mathrm{J}$, where $x$ is in $\mathrm{metre}$. It can be concluded that the wrong option is

In a gravitational force field a particle is taken from $A$   to $B$ along different paths as shown in figure. Then

Assertion: Friction is a conservative force.
Reason: Friction does not depend upon mass of the body.

Frictional force is_______________.

Which of the following statement is not true?

The potential energy of a system increases if work is done

Which of the following is true for an Unstable equilibrium ?

The potential energy of a particle under a conservative force is given by $U\left(x\right)=\left(x^2-3x\right) \mathrm{J}$. The equilibrium position of the particle is at:

If the potential energy for the force between two atoms in a diatomic molecule is given by $U$$\left(x\right)=\frac{a}{x^{12}}$$-\frac{b}{x^6}$, given $a$ and $b$ are constants $x=$ atomic distance, What is the value of $D$ if  the dissociation energy of the molecule is $D=\left[U\left(x=\infty \right)-U_{\mathrm{at} \mathrm{equilibrium}}\right]$?

Example of a non-conservative force is:

When a block moves with some friction on ground,

The given plot shows the variation of $\mathrm{U}$, the potential energy of interaction between two particles with the distance separating them $\mathrm{r}$.

1. $\mathrm{B}$ and $\mathrm{D}$ are equilibrium points

2. $\mathrm{C}$ is a point of stable equilibrium

3. The force of interaction between the two particles is attractive between points $\mathrm{C}$ and $\mathrm{D}$ and repulsive between $\mathrm{D}$ and $\mathrm{E}$

4. The force of interaction between particles is repulsive between points $\mathrm{E}$ and $\mathrm{F}$.

Which of the above statements is correct?

Select the correct Potential energy($U$) vs inter-atomic distance($r$) for a stable molecules found in nature.