Potential Energy

If potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left(x\right)=\frac{\mathrm{a}}{x^8}-\frac{\mathrm{b}}{x^4}$, where $\mathrm{a}$ and $\mathrm{b}$ are constants in standard SI units and $x$ is in metres. Find the dissociation energy of the molecule (in $\mathrm{J}$). [Take $\mathrm{a}=4 \mathrm{J} {\mathrm{m}}^8$ and $\mathrm{b}=20 \mathrm{J} {\mathrm{m}}^4$]

Which of the following is true for an Unstable equilibrium ?

For unstable equilibrium,the second derivative should be Negative. 

A system in _____ equilibrium accelerates away from its equilibrium position if displaced even slightly.

A rectangle block rests on a horizontal table. A horizontal force is applied on the block at a height $h$ above the table to move the block. Does the line of action of the normal force $N$ exerted by the table on the block depend on $h$?

For equilibrium, the net moment acting on the body by various forces is zero.

The energy of a body due to its position or change in shape is known as _____energy. 

Formula for potential energy is_____.

Water stored in a dam posseses

A body is falling from a height h. After it has fallen a height h/2, it will possess_____.

Water stored in a dam possesses_____.

A car is accelerated on a levelled road and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car_____.

The energy possessed by a body due to its position is called

If mass of an object, m = 10 kg, displacement (height) h = 6m, and acceleration due to gravity, g = 9.8 ms^-2. Then potential energy is  

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?

$U\left(x\right)=\frac{a}{x^{12}}-\frac{b}{x^6}$ represents the potential energy between two atoms in a molecule, where $x$ is the distance between the atoms and $A$ and $B$ are positive. The atom will be in stable equilibrium if

A particle of mass$m = 1 \mathrm{kg}$ lying on$x$ axis experiences a force given by law, $F=x(3x-2) \mathrm{N}$, where $x$ is the coordinate of the particle in $\mathrm{meters}$.

In a uniform magnetic field of 0.15 T a short bar magnet of magnetic moment m = 0.32 J/T is placed. What is the potential energy of the magnet in unstable position , if the bar is free to rotate in the plane of the field?

In the arrangements shown below, all the balls are identical and strings are light. There is no friction. In each of the three arrangements $A, B$ and $C$, the system is in equilibrium.
 
The hill slopes are identical on the two slides in each of the arrangements.
One of the balls in each arrangement is pulled down a little along the hill slope.

An adult weighing $600\mathrm{ }\mathrm{N}$ raises the centre of gravity of his body by $0.25 \mathrm{m}$ while taking each step of $1 \mathrm{m}$ length in jogging. If he jogs for $6 \mathrm{km}$, the energy utilised by him in jogging is