Potential Energy

Select the correct alternative: When a conservative force does positive work on a body, the potential energy of the body _____.

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 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

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

A block of mass $10 \mathrm{k}\mathrm{g}$ is kept on a rough inclined plane as shown in the figure. The coefficient of friction between the block and the surface is $0.6$ . Two forces of magnitude $3\mathrm{N}$ and P Newton are acting on the block. If friction on the block is acting upwards then minimum value of P for which the block remains at rest is:

In the following diagrams, a particle with small charge - q is free to move up or down, but not sideways near a larger fixed charge Q. The small charge is in equilibrium because in the positions shown, the electrical upward force is equal to the weight of the particle. Which statement is true?

If a man having bag in his hand moves up on a stair. Then

A ball is dropped from a height of $20\mathrm{ }\mathrm{c}\mathrm{m}$. Ball rebound to a height of $10\mathrm{ }\mathrm{c}\mathrm{m}$. What is the loss of energy?

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

To the free end of spring hanging from a rigid support, a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then stretching in the spring is $d$. if the same block is attached to the same spring and allowed to fall suddenly, the amount of stretching is (force constant, $k$)

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be