Ratio of Linear Momenta – Rankers Physics
Topic: Work Energy and Power
Subtopic: Kinetic Energy and Momentum

Ratio of Linear Momenta

Two masses \(1\text{ g}\) and \(9\text{ g}\) are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is
\(1 : 9\)
\(9 : 1\)
\(1 : 3\)
\(3 : 1\)

Solution:

Since linear momentum \(p = \sqrt{2mK}\) and kinetic energy \(K\) is constant, \(p \propto \sqrt{m}\). Therefore, the ratio of momenta is \(\frac{p_1}{p_2} = \sqrt{\frac{1}{9}} = 1:3\).

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