Question

If the kinetic energy of a moving body becomes four times of its initial value. The new linear momentum will be

• A. Eight times of the initial value
• B. Four times of the initial value
• C. Two times of the initial value
• D. Remains the same

Answer 1

Answer:

C. Two times of the initial value

Physics Principles of Momentum and Kinetic Energy

• Relationship Equation: The relationship between Kinetic Energy (KE) and linear momentum (p) is defined by the formula KE = p² / (2m), where m represents the mass of the body.

• Derivation: Since KE is proportional to the square of momentum (KE ∝ p²), it implies that momentum is proportional to the square root of kinetic energy (p ∝ √KE).

• Calculation Steps: If the initial kinetic energy is KE1 and the final is KE2 = 4 × KE1, the ratio of the new momentum (p2) to the initial momentum (p1) is determined as:

  • p2 / p1 = √(KE2 / KE1)

  • p2 / p1 = √(4 × KE1 / KE1)

  • p2 / p1 = √4

  • p2 / p1 = 2

• Conclusion: Therefore, the new linear momentum becomes 2 times the initial linear momentum.