Question

two bodies of equal masses move with uniform velocities V and 3V respwctively.find the ratio of their kinetic energies

Answer 1

Let the mass of each body be 'm'.
The kinetic energy is given as:
$K.E=\frac{1}{2}m{V}^2$
Kinetic energy of mass 1,
$K.E_1=\frac{1}{2}m{V}^2$
Kinetic energy of mass 2,
$$\begin{gathered} K.E_2=\frac{1}{2}m(3V{)}^2=9\times \frac{1}{2}m{V}^2=9\times K.E_1 \\ \Rightarrow \frac{K.E_2}{K.E_1}=9 \\ \Rightarrow \frac{K.E_1}{K.E_2}=\frac{1}{9} \end{gathered}$$
This is the required ratio of the kinetic energy of the two masses.