$A$ stretched rubber band has:

$A$ particle which is constrained to move along the $x-$axis is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin as $F(x) = -kx + ax^3$. Here $k$ and $a$ are positive constants. For $x \ge 0$,the functional form of the potential energy $U(x)$ of the particle is

The following figure shows the variation of potential energy $V(x)$ of a particle with distance $x$. The particle has

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

Potential energy is a......

Potential energy of a particle varies with position $r$ as,$U = \left( \frac{\alpha}{r^4} - \frac{\beta}{r^5} \right) \text{ J}$,where $\alpha$ and $\beta$ are positive constants. The particle will be in equilibrium at $r = \dots$