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

Answer»

Here, pi = pz , 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.


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