Law of Conservation of Energy

What happens if a body falls towards the earth?

Total energy of an isolated system-

A ball is thrown vertically up with a velocity $20 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$. At what height will its kinetic energy be half its original value?

An object is dropped from a certain distance when she is at half distance she is ______ in it?

A $U-$shaped smooth wire has a semi-circular bend of radius $R$ between $A$ and $B$. It is held fixed in a vertical plane. A bead of mass $m$ is released from height $h$ (above $A$) and slides smoothly along the wire to reach the same height on other side of the wire. It is given that $h\gg R$.

Consider the motion of the bead between $A$ and the lowest point $C$ of the wire. The ratio of change in magnitude of velocity of the particle at $A$ to the magnitude of change in its velocity at $C$ is nearly equal to

A U-tube of cross section $\mathrm{A}$ and $2\mathrm{A}$ as shown contains liquid of density $\mathrm{d}$. Initially, the liquid in the two arms are held with a level difference $\mathrm{h}$. After being released the levels equalize after some time. The work done by gravity forces on the liquid in the process is -

A ball of mass $2 \mathrm{kg}$ and another of mass $4 \mathrm{kg}$ are dropped together from a $60$ feet tall building. After a fall of $30$ feet each towards earth, their respective kinetic energies will be in the ratio of