Kinetic Energy and Momentum: Practice Problem & Solution

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:

Concept: Relation between kinetic energy and momentum. Formula: \(KE = \frac{p^2}{2m}\). Given \(KE_1 = KE_2\), so \(\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}\). This implies \(\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}}\). Substituting \(m_1 = 1\text{ g}\) and \(m_2 = 9\text{ g}\), we get \(\frac{p_1}{p_2} = \sqrt{\frac{1}{9}} = \frac{1}{3}\). Thus the ratio is \(1:3\).