$A$ particle with constant total energy $E$ moves in one dimension in a region where the potential energy is $U(x)$. The speed of the particle is zero where

The work done in pumping out water from a cubical vessel of height $1 \ m$ is approximately ........ $J$ (Take $g = 10 \ m/s^2$ and density of water $\rho = 1000 \ kg/m^3$).

In the equation $W = -mgh$,what does the negative sign indicate?

$A$ body at rest may have

The potential energy $(U)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U = \frac{\alpha}{r^{10}} - \frac{\beta}{r^5} - 3$,where $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be $\left(\frac{2\alpha}{\beta}\right)^{\frac{a}{b}}$,where $a = \dots \dots \dots \dots$

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