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Q86 (CDS-II/2020) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

If the linear momentum of a moving object gets doubled due to application of a force, then its kinetic energy will

Result
Your answer: —  Â·  Correct: B
Explanation

The relationship between kinetic energy (KE) and linear momentum (p) is defined by the formula KE = p" / (2m), where 'm' represents the mass of the object. This mathematical relationship indicates that kinetic energy is directly proportional to the square of the momentum. When the linear momentum of a moving object is doubled (p' = 2p), the new kinetic energy becomes (2p)" / (2m), which simplifies to 4 * (p" / 2m). Consequently, doubling the momentum results in the kinetic energy increasing by a factor of four. This occurs because while momentum increases linearly with velocity, kinetic energy increases as the square of the velocity. Therefore, if a force acts on an object such that its momentum is doubled, its kinetic energy will increase by four times.

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