If the linear momentum of a moving object gets doubled due to applicat

by

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

remain same
increase by four times
increase by two times
increase by eight times
This question was previously asked in
UPSC CDS-2 – 2020
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The kinetic energy of the moving object will increase by four times.
The linear momentum (p) of an object is given by the product of its mass (m) and velocity (v), i.e., p = mv. The kinetic energy (KE) is given by KE = (1/2)mv². We can express KE in terms of momentum: KE = (1/2)m(p/m)² = p²/(2m). If the momentum is doubled (p’ = 2p), the new kinetic energy (KE’) will be KE’ = (p’)²/(2m) = (2p)²/(2m) = 4p²/(2m) = 4 * (p²/(2m)) = 4 * KE.
This relationship shows that kinetic energy is proportional to the square of momentum when mass is constant. Doubling the momentum results in quadrupling the kinetic energy.

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