Question

4. Two masses m1 and m2, with m1 < m2, have momenta with equal magnitudes. How do their kinetic energies compare

Answer 1

Answer:

E₁ > E₂

Explanation:

Given,

Mass of objects = m₁ and m₂ such that m₁ < m₂

Momentum of the two bodies are equal.

Lets assume they are moving with velocity v₁ and v₂ respectively.

Thus momentum of first body (P₁)= m₁v₁

and momentum of second body (P₂) = m₂v₂

Since,

P₁ = P₂

m₁v₁ = m₂v₂

Given that m₁ < m₂,

it is clear that v₁ > v₂.

Now, Kinetic energy of an object is given as,

$E = \frac{1}{2} mv^{2}$

$E₁ = \frac{1}{2} m₁v₁^{2}$

$E₂ = \frac{1}{2} m₂v₂^{2}$

Since, v₂ < v₁,

E₁ > E₂