While a person climbs stairs,the gravitational potential energy of the person increases. The source of this energy is

$A$ point particle of mass $0.5 \,kg$ is moving along the $X$-axis under a force described by the potential energy $V$ shown in the graph. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\text{at equilibrium}}]$,then $D$ is:

$A$ uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table? (Take $g = 10\,m/s^2$)

The diagrams represent the potential energy $U$ as a function of the inter-atomic distance $r$. Which diagram corresponds to stable molecules found in nature?

$A$ uniform chain of length $l$ and mass $m$ lies on the surface of a smooth hemisphere of radius $R$ $(R > l)$ with one end tied to the top of the hemisphere as shown in the figure. Gravitational potential energy of the chain with respect to the base of the hemisphere is