Potential Energy

Differentiate between stable, unstable and neutral equilibrium.

What is potential energy?

A ball of mass $0.1 \mathrm{kg}$ is thrown vertically upwards with a velocity of $20 \mathrm{m}/\mathrm{s}$. What is the potential energy at the maximum height? What is the potential energy of the ball when it reaches three-quarters of the maximum height while moving upwards?

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 ($g= 10 \mathrm{m}/{\mathrm{s}}^2$)

Potential energy is defined for a system whose elements interact via conservative force. A hypothetical system has potential energy corresponding to a conservative force given as $U= 7x^{2}y-2x$. Find the force on the system corresponding to the above energy function.

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?

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.

Which tense is used in the sentence: 'She will have finished her work by tomorrow'?

Who is the head of the executive branch in India?

Which factor is NOT typically considered when choosing a source of funds?

Which committee recommended the establishment of Nyaya Panchayats to deliver justice in rural areas?

Which of the following is an example of internal source of funds?

In which sentence is the use of the modifier 'never' correctly emphasizing the verb 'speaks'?

Identify the sentence where the modifier 'quickly' is correctly placed to emphasize the verb 'finished'.

Which of the following is NOT a common feature of e-commerce platforms?