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: Establish the relationship between kinetic energy and momentum.
The kinetic energy \( KE \) is defined in terms of momentum \( p \) as follows:\[KE = \frac{p^2}{2m}\]Where:- \( p \) represents the momentum,- \( m \) represents the mass of the body.Step 2: Evaluate the specified scenario. Given that the kinetic energy is quadrupled:\[4 \times KE_0 = \frac{(2p_0)^2}{2m}\]This indicates that the final momentum \( p \) is twice the initial momentum \( p_0 \).Step 3: Final Statement The resulting momentum is double the original momentum. Final Answer: \[ \boxed{2 \, \text{times the initial value}}\]