Question

A light body and a heavy body have same linear momentum. Which one has greater K.E.?

Answer 1

Here, p_i = p_z , m₁v₁ = m₂v₂

∴ \(\frac{v_2}{v_1}=\frac{m_1}{m_2}..........(i)\)

As \(E_2=\frac{1}{2}m_2v^2_2\)

and \(E_1=\frac{1}{2}m_1v^2_1\)

∴ \(\frac{E_2}{E_1}=\frac{\frac{1}{2}m_2v^2_2}{\frac{1}{2}m_1v^2_1}\)

\(=\frac{m_2}{m_1}(\frac{v_2}{v_1})^2\)

using (i) \(\frac{E_2}{E_1}=\frac{m_2}{m_1}\times(\frac{m_1}{m_2})^2\)

If m₁ < m₂, E₂ < E₁

or E₁ > E₂

i. e., lighter body has more K.E.