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:

Kinetic energy \(KE = \frac{p^2}{2m}\), so momentum \(p = \sqrt{2mKE}\). Given \(KE_1 = KE_2 = KE\). For the two bodies, \(p_1 = \sqrt{2mKE}\) and \(p_2 = \sqrt{2(4m)KE}\). The ratio of their linear momenta is \(\frac{p_1}{p_2} = \frac{\sqrt{2mKE}}{\sqrt{8mKE}} = \sqrt{\frac{1}{4}} = \frac{1}{2}\). So, the ratio is \(1:2\).