CAPF AC 2022 Q27: Science & Technology – Physics
If the linear momentum of a moving object changes by two times, then its kinetic energy will change by a factor of
- (a) 2
- (b) 4
- (c) 6
- (d) 8
Answer: (b) 4
Explanation
Momentum and kinetic energy
Given: the linear momentum of a moving object changes by two times; find the factor by which its kinetic energy changes.
How to think: write kinetic energy in terms of momentum.
For a fixed mass, kinetic energy depends on the square of the momentum.
| Step | Working |
|---|---|
| Momentum | p = mv |
| Kinetic energy | K = (1/2)mv² = p²/2m |
| Momentum doubles | p → 2p |
| New kinetic energy | (2p)²/2m = 4 × p²/2m |
So the kinetic energy becomes 4 times.
Answer: (b) 4.
Why each option is right or wrong
- (a) Incorrect. A factor of 2 forgets that momentum is squared in the formula.
- (b) CORRECT. K = p²/2m, so doubling p makes K 4 times.
- (c) Incorrect. 6 does not follow from any power of 2.
- (d) Incorrect. 8 would need the cube of the momentum.
Key point
K = p²/2m and p = √(2mK). For constant mass, K ∝ p². Momentum × 2 → K × 4; momentum × 3 → K × 9.
Remember
K = p²/2m: double p, four times K.
Common mistakes
- Taking kinetic energy as directly proportional to momentum.
- Forgetting the relation K = p²/2m and trying to guess.
- Thinking the mass changes when the momentum changes.
Exam tip
Educated guess: for a fixed mass, doubling momentum means doubling the speed. Kinetic energy goes with speed squared, so it becomes four times.
Sources
- NCERT Class IX Science — Work and Energy; Force and Laws of Motion (momentum)
- NCERT Class XI Physics — Work, Energy and Power