Question

If the kinetic energy of the body with constant mass becomes four times the initial value, then the new momentum will be:

• A. four times the initial value
• B. three times the initial value
• C. two times the initial value
• D. same as the initial value

Hint:

The kinetic energy is proportional to the square of the momentum. If kinetic energy increases by a factor of 4, momentum increases by a factor of (B)

Answer 1

The Correct Option is C

Step 1: Relate kinetic energy and momentum.
The kinetic energy \( KE \) is related to momentum \( p \) by the equation: \[ KE = \frac{p^2}{2m} \] Where: - \( p \) is the momentum, - \( m \) is the mass of the body. Step 2: Analyze the given condition. If the kinetic energy becomes four times its initial value: \[ 4 \times KE_0 = \frac{(2p_0)^2}{2m} \] This shows that the new momentum \( p \) is twice the initial momentum \( p_0 \). Step 3: Conclusion The new momentum is twice the initial momentum. Final Answer: \[ \boxed{2 \, \text{times the initial value}} \]