Question

A light and a heavy object have the same momentum, find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

August 6, 2024

Answer

Linear momentum of first object, 𝑝₁ = 𝑚₁𝑣₁and of second object, 𝑝₂= 𝑚₂𝑣₂

But, 𝑝₁ = 𝑝₂

or, 𝑚₁𝑣₁ = 𝑚₂𝑣₂

If 𝑚₁ < 𝑚₂ then 𝑣₁ > 𝑣₂

(K.E.)₁ = ${1\over2}$ (𝑚₁𝑣₁)𝑣₁ = ${1\over2}$ 𝑝₁𝑣₁

and (K.E.)₂ = ${1\over2}$ (𝑚₂𝑣₂)𝑣₂ = ${1\over2}$ 𝑝₂𝑣₂

So, ${({K.E.})_1}\over{({K.E.})_2}$ = ${{1\over2}p_1v_1}\over{{1\over2}p_2v_2}$ = ${v_1\over v_2}$

But, 𝑣₁ > 𝑣₂

Therefore, (K.E.)₁ > (K.E.)₂

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