Stationary particle explosion – Rankers Physics

Kinetic Energy and Momentum: Practice Problem & Solution

A stationary particle explodes into two particles of masses \(m_1\) and \(m_2\) which move in opposite directions with velocities \(v_1\) and \(v_2\). The ratio of their kinetic energies \(E_1/E_2\) is: (2003)
\(m_2/m_1\)
\(m_1/m_2\)
\(1\)
\(m_1 v_2 / m_2 v_1\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Kinetic Energy and Momentum. Understanding the underlying formula is key to arriving at the correct answer below:

By conservation of momentum, since the initial particle is stationary, \(m_1v_1 = m_2v_2\) (in magnitude). This means their momenta are equal in magnitude: \(p_1 = p_2 = p\). Kinetic energy \(E = \frac{p^2}{2m}\). So \(E_1 = \frac{p^2}{2m_1}\) and \(E_2 = \frac{p^2}{2m_2}\). The ratio \(\frac{E_1}{E_2} = \frac{p^2/(2m_1)}{p^2/(2m_2)} = \frac{m_2}{m_1}\).

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