The potential energy of a particle is given by $U = 8x^2 - 4x + 400 \, J$. Find the position $x$ where the force acting on the particle is zero.

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?

$A$ mass of $M \ kg$ is suspended by a weightless string of length $\ell$. The horizontal force required to displace it until the string makes an angle of $45^\circ$ with the initial vertical direction is:

$A$ body at rest may have

Potential energy as a function of $r$ is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$,where $r$ is the interatomic distance,and $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be

If a stone is thrown vertically upward and returns to the ground,its potential energy is maximum: