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:

Calculate the work done by pump $P$ to transfer water of density $d$ from one container to another as shown in the figure.

$A$ uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $(1/n)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface,the work done should be

$A$ particle is released from rest at the point $x = a$ and moves along the $x$ axis subject to the potential energy function $U(x)$ shown. The particle:

If an object of mass $20 \ g$ falls from a height of $200 \ m$,and at the point where the object touches the Earth's surface,its total potential energy is converted into kinetic energy,then what is the decrease in the potential energy of the object in $J$?

The potential energy of a diatomic molecule is given by $U = \frac{A}{r^{12}} - \frac{B}{r^6}$,where $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is: