Question

If two bodies of equal masses move with uniform velocity of '$v$' and '$3v$', what will be the ratio of their kinetic energies?

Answer 1

Mass of first body $=m$
Velocity of the first body $=v$
Mass of second body $=m$
Velocity of second body $=3v$
The ratio of kinetic energies of the two bodies $=\frac{Kineticenergiesoffirstbody}{Kineticenergiesofsecondbody}$
$=\frac{\frac{1}{2}m{v}^2}{\frac{1}{2}m{\left(3v\right)}^2}=\frac{\frac{1}{2}m{v}^2}{\frac{9}{2}m{v}^2}$
$=\frac{1}{9}$
The ratio of the kinetic energies $=1:9$