The potential energy of a body is given by $U = A - Bx^2$ (where $x$ is the displacement). The magnitude of the force acting on the particle is:

The decrease in the potential energy of a ball of mass $20 \,kg$ which falls from a height of $50 \,cm$ is ............ $J$.

If the potential energy between two molecules is given by $U = -\frac{A}{r^6} + \frac{B}{r^{12}}$,then at equilibrium,the separation between the molecules and the potential energy are:

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 $\rho = 1000 \ kg/m^3$).

$A$ 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

If a body of mass $200\, g$ falls from a height $200\, m$ and its total $P.E.$ is converted into $K.E.$ at the point of contact of the body with the earth's surface,then what is the decrease in $P.E.$ of the body at the contact? $(g = 10\, m/s^2)$ ............ $J$