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Work, Energy and Power is the chapter that lets you skip the hard part. A question that would take half a page with Newton’s laws often takes two lines with the work–energy theorem, because energy does not care about the path taken. Learning to spot which questions are energy questions is worth more here than any single formula. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 2 questions every year, which is 8 marks.
- The work–energy theorem and spring energy are the regular ones.
- Power, collisions and conservative forces fill the rest.
What the syllabus says
In the syllabus (Unit 4, Work, Energy and Power): Work done by a constant force and by a variable force, kinetic and potential energy, the work–energy theorem, power, potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces, motion in a vertical circle, elastic and inelastic collisions in one and two dimensions.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Work done by a constant force | W = F·d = Fd cosθ |
| Work done by a variable force | W = ∫ F dx |
| Kinetic energy | KE = ½mv2 = p2/2m |
| Work–energy theorem | Wnet = ΔKE |
| Gravitational potential energy | U = mgh |
| Energy stored in a spring | U = ½kx2 |
| Power | P = W/t = F·v |
| Conservative force | the work done depends only on the end points |
| Elastic collision | both momentum and kinetic energy are conserved |
| Inelastic collision | momentum is conserved, kinetic energy is not |
The form KE = p2/2m is the one to reach for whenever a question talks about momentum and energy together. It makes it obvious at once that doubling the momentum makes the kinetic energy four times larger.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. A force F = (3î + 4ĵ) N moves a body through a displacement d = (2î + 3ĵ) m. The work done is
- (a) 6 J
- (b) 12 J
- (c) 18 J
- (d) 25 J
Q2. The work–energy theorem says that the net work done on a body equals the change in its
- (a) momentum
- (b) kinetic energy
- (c) potential energy
- (d) power
Q3. A spring of force constant 200 N/m is stretched by 10 cm. The energy stored in it is
- (a) 0.5 J
- (b) 1 J
- (c) 2 J
- (d) 10 J
Q4. A body of mass 2 kg moves with a speed of 10 m/s. Its kinetic energy is
- (a) 20 J
- (b) 100 J
- (c) 200 J
- (d) 10 J
Q5. If the momentum of a body is doubled, its kinetic energy becomes
- (a) double
- (b) four times
- (c) half
- (d) unchanged
Q6. A pump raises 100 kg of water through 10 m in 10 s. Taking g = 10 m/s2, its power output is
- (a) 100 W
- (b) 1000 W
- (c) 10000 W
- (d) 10 W
Q7. A force is called conservative when the work it does
- (a) depends on the path taken
- (b) depends only on the starting and finishing points
- (c) is always zero
- (d) is always negative
Q8. In a perfectly elastic collision, the quantities conserved are
- (a) momentum only
- (b) kinetic energy only
- (c) both momentum and kinetic energy
- (d) neither of them
Q9. A body falls freely from a height h. Its kinetic energy equals its potential energy at a height of
- (a) h/4
- (b) h/2
- (c) 3h/4
- (d) h
Q10. The work done by the centripetal force on a body completing one full circle is
- (a) 2πrF
- (b) zero
- (c) Fr
- (d) πrF
Answer key, with a hint for each
| Q1 | (c) | W = F·d = 3(2) + 4(3) = 6 + 12. |
| Q2 | (b) | Not potential energy. That is the commonest slip in this chapter. |
| Q3 | (b) | U = ½kx2 = ½ × 200 × (0.1)2. Convert the centimetres first. |
| Q4 | (b) | ½ × 2 × 100. |
| Q5 | (b) | KE = p2/2m, so the energy goes as the square of the momentum. |
| Q6 | (b) | P = mgh/t = 100 × 10 × 10 / 10. |
| Q7 | (b) | Gravity and the spring force are conservative. Friction is not, which is why friction always costs you energy. |
| Q8 | (c) | That is what elastic means. In an inelastic collision only the momentum survives. |
| Q9 | (b) | Half the total energy must be kinetic, and the body has fallen half the height by then. |
| Q10 | (b) | The force points to the centre and the motion is along the circle, so the two are always at right angles. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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