Question

Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momentum of B to A is

• A. 1 : 3
• B. 1 : \( \sqrt{3} \)
• C. 1 : \( \sqrt{5} \)
• D. \( \sqrt{3} \) : 1

Hint:

For bodies with equal kinetic energy, the ratio of their momenta is inversely proportional to the square root of the mass ratio.

Answer 1

The Correct Option is B

Step 1: Write the equation for kinetic energy.
Kinetic energy is given by \( KE = \frac{p^2}{2m} \), where \( p \) is momentum and \( m \) is mass. Since \( KE_A = KE_B \), we have: \[ \frac{p_A^2}{2m_A} = \frac{p_B^2}{2m_B} \]
Step 2: Solve for the ratio of momenta.
From the above equation, we get: \[ \frac{p_B}{p_A} = \sqrt{\frac{m_A}{m_B}} = \sqrt{3} \]
Final Answer: \[ \boxed{1 : \sqrt{3}} \]