If the linear momentum of a moving object changes by two times, then its kinetic energy will change by a factor of
2
4
6
8
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2022
Kinetic energy (k) of the same object is given by k = ½ mv².
We can express kinetic energy in terms of momentum. From p = mv, we get v = p/m. Substituting this into the kinetic energy equation:
k = ½ m(p/m)² = ½ m(p²/m²) = ½ p²/m.
So, k is proportional to p² (assuming mass m is constant).
If the initial momentum is p₁, the initial kinetic energy is k₁ = ½ p₁²/m.
If the linear momentum changes by two times, it means the new momentum p₂ = 2p₁.
The new kinetic energy k₂ = ½ p₂²/m = ½ (2p₁)²/m = ½ (4p₁²)/m = 4 (½ p₁²/m) = 4k₁.
Thus, the kinetic energy will change by a factor of 4.