Question

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

• A. \(1 : \sqrt{3} : 2\)
• B. \(1 : \sqrt{3} : \sqrt{2}\)
• C. \(\sqrt{2} : \sqrt{3} : 1\)
• D. \(\sqrt{3} : \sqrt{2} : 1\)

Answer 1

The Correct Option is A

The kinetic energy is given by:
\[ KE = \frac{P^2}{2m}, \quad \text{where } P \propto \sqrt{m}. \]
For masses \(m_A = 400 \, \text{g}, \, m_B = 1.2 \, \text{kg}, \, m_C = 1.6 \, \text{kg}\):
\[ P_A : P_B : P_C = \sqrt{400} : \sqrt{1200} : \sqrt{1600}. \]
Simplify:
\[ P_A : P_B : P_C = 1 : \sqrt{3} : 2. \]
Final Answer: 1 : \(\sqrt{3}\) : 2.