Question

Two bodies of mass 1 Kg and 9 Kg are moving with same velocity . What is the ratio of their kinetic energy?

Answer 1

Given,
Mass of bodies,
m=1 kg and m'=9 kg
Velocities of bodies,
v=v and v'=v (Both are moving with same velocities)
$$\begin{gathered} \mathrm{Kinetic}\mathrm{energies}\mathrm{are}\mathrm{given}\mathrm{by}, \\ \mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2=\frac{1}{2}\times 1\times {\mathrm{v}}^2=\frac{{\mathrm{v}}^2}{2}----\left(\mathrm{i}\right) \\ \mathrm{K}\text{'}=\frac{1}{2}\mathrm{m}\text{'}\mathrm{v}{\text{'}}^2=\frac{1}{2}\times 9\times {\mathrm{v}}^2=\frac{9{\mathrm{v}}^2}{2}---\left(\mathrm{ii}\right) \\ \mathrm{Now}, \\ \frac{\mathrm{K}}{\mathrm{K}\text{'}}=\frac{{\mathrm{v}}^2}{2}/\frac{9{\mathrm{v}}^2}{2}=\frac{1}{9} \\ \mathrm{or}\mathrm{K}:\mathrm{K}\text{'}=1:9 \end{gathered}$$