Question

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is:

• A. 3 : 5
• B. 5 : 4
• C. 2 : 5
• D. 4 : 5

Hint:

For objects with equal kinetic energy, the ratio of their momentum is given by \( \frac{P_1}{P_2} = \sqrt{\frac{m_1}{m_2}} \).

Answer 1

The Correct Option is C

Step 1: Formula for Linear Momentum
The linear momentum \( P \) of an object is given by: \[ P = \sqrt{2 m E} \] where \( m \) is the mass and \( E \) is the kinetic energy.
Step 2: Relationship Between Momentum and Mass
Given that the kinetic energies of the two masses are equal, we equate: \[ E_1 = E_2 \quad \Rightarrow \quad \frac{P_1^2}{2m_1} = \frac{P_2^2}{2m_2} \]
Rearranging: \[ \frac{P_1}{P_2} = \sqrt{\frac{m_1}{m_2}} \]
Step 3: Substituting Values
Given \( m_1 = 4 \) g and \( m_2 = 25 \) g, we substitute: \[ \frac{P_1}{P_2} = \sqrt{\frac{4}{25}} = \frac{2}{5} \] Final Answer: The ratio of the magnitudes of their linear momentum is 2:5.