CAPF AC 2022 Q20: Science & Technology – Physics
Two objects, x and y, have equal mass and are moving with speeds u and 3u respectively. Their kinetic energies kx and ky are related as
- (a) kx = ky
- (b) 2kx = ky
- (c) 9kx = ky
- (d) 3kx = ky
Answer: (c) 9kx = ky
Explanation
Kinetic energy and speed
Given: two objects x and y have equal mass and move with speeds u and 3u; relate their kinetic energies kx and ky.
How to think: kinetic energy depends on the square of the speed.
If the speed is 3 times, the energy is 3² = 9 times.
| Object | Speed | Kinetic energy |
|---|---|---|
| x | u | kx = (1/2) m u² |
| y | 3u | ky = (1/2) m (3u)² = 9 × (1/2) m u² |
So ky = 9 kx.
Answer: (c) 9kx = ky.
Why each option is right or wrong
- (a) Incorrect. Equal energies would need equal speeds.
- (b) Incorrect. A factor of 2 does not come from a speed ratio of 3.
- (c) CORRECT. Speed is 3 times, so kinetic energy is 3² = 9 times.
- (d) Incorrect. A factor of 3 forgets that speed is squared; that is the rule for momentum.
Key point
Kinetic energy = (1/2)mv². Doubling the speed gives 4 times the energy; tripling gives 9 times. Momentum = mv rises only in direct proportion.
Remember
Speed × 3 → kinetic energy × 9.
Common mistakes
- Forgetting to square the speed and answering 3 times.
- Mixing up kinetic energy with momentum, which is proportional to speed.
- Reading the relation backwards as kx = 9ky.
Exam tip
Educated guess: the word energy with speed always means square. Three squared is nine.
Sources
- NCERT Class IX Science — Work and Energy (kinetic energy)
- NCERT Class XI Physics — Work, Energy and Power