Question

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger K.E?

Answer 1

Dear Student,

Let the two bodies have masses m₁ and m₂ such that m₁ < m₂ . Then, for 1^st object P₁ = m₁v₁ and for 2^nd object P₂ = m₂v₂
But P₁ = P₂ or m₁v₁ = m₂v₂
Since m₁ < m₂, then v₁ > v₂
Now, K.E. = $\frac{1}{2}$ mv² = $\frac{1}{2}$ Pv, therefore,
$\frac{\mathrm{K}.{\mathrm{E}}_1}{\mathrm{K}.{\mathrm{E}}_2}=\frac{{\mathrm{P}}_1{\mathrm{v}}_1}{{\mathrm{P}}_2{\mathrm{v}}_2}=\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}[\mathrm{since}{\mathrm{P}}_1={\mathrm{P}}_2]$
But v₁ > v₂
Therefore, kinetic energy of body of lesser mass is more, i.e. of mass m₁.

regards