Question

relate the mass,kinetic energy and momentum of an object.

Answer 1

Momentum, p=mass (m) x velocity (v)----(i)
Kinetic energy,K=$\frac{1}{2}{\mathrm{mv}}^2$----(ii)
Squaring equation (i),
${\mathrm{p}}^2={\mathrm{m}}^2{\mathrm{v}}^2$---(iii)
In (ii),
Multiplying and dividing by m
$\mathrm{K}=\frac{1}{2}\frac{{\mathrm{m}}^2{\mathrm{v}}^2}{\mathrm{m}}----\left(\mathrm{iv}\right)$
So,
$$\begin{gathered} \mathrm{K}=\frac{1}{2}\frac{{\mathrm{p}}^2}{\mathrm{m}} \\ \mathrm{K}=\frac{{\mathrm{p}}^2}{2\mathrm{m}} \end{gathered}$$