Work, Power & Energy
Solve official JEE Main Work, Power & Energy chapter-wise PYQs online. Work-energy theorem, spring potential energy, collisions & detailed solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Work, Power & Energy:
- Work Done by Constant & Variable Forces (W = ∫ F · dx)
- Work-Energy Theorem: W_net = ΔKE = ½ m v² - ½ m u²
- Conservative Forces & Potential Energy (F = -dU/dx)
- Elastic & Inelastic Collisions in 1D & 2D (Coefficient of Restitution e)
- Power P = F · v = dW/dt
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Work & Energy questions in under 45 seconds:
Spring Potential Energy: U = ½ k x².
Stable Equilibrium: dU/dx = 0 and d²U/dx² > 0 (Potential energy minimum).
1D Elastic Head-on Collision with equal masses (m₁ = m₂): Velocities simply swap.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 6 J
- Step 1: Work done by a variable force is W = ∫ F dx.
- Step 2: W = ∫₀² (3x² - 2x + 1) dx.
- Step 3: Integrate term by term: [x³ - x² + x]₀².
- Step 4: Substitute limits: (2³ - 2² + 2) - 0 = 8 - 4 + 2 = 6 J.
⚡ Speed Tip: Variable Work Integration: [x³ - x² + x] from 0 to 2 = 8 - 4 + 2 = 6 J.
💡 View Step-by-Step Solution & Answer
Correct Answer: 100%
- Step 1: Relation between kinetic energy and momentum: KE = p² / (2m) ⇒ p = √(2m · KE).
- Step 2: A 300% increase means the new kinetic energy is KE' = KE + 3(KE) = 4 KE.
- Step 3: New momentum is p' = √(2m · 4KE) = 2 · √(2m · KE) = 2p.
- Step 4: Percentage increase in momentum = ((p' - p) / p) × 100% = ((2p - p) / p) × 100% = 100%.
⚡ Speed Tip: Square Root Scaling: Momentum scales as √KE. If KE becomes 4×, momentum becomes 2× (+100%).
💡 View Step-by-Step Solution & Answer
Correct Answer: ½ m v³
- Step 1: Mass of water flowing out per unit time: dm/dt = m · v (mass per unit length × velocity).
- Step 2: Kinetic energy imparted per unit time is Power = d(KE)/dt = ½ (dm/dt) v².
- Step 3: Substitute dm/dt = m v: Power = ½ (m v) v².
- Step 4: Power = ½ m v³.
⚡ Speed Tip: Continuous Flow Power: P = ½ (dm/dt) v² = ½ (mv) v² = ½ m v³.
❓ Frequently Asked Questions (FAQs)
What is the condition for complete vertical circle looping?
Minimum velocity at lowest point for a string must be v_min = √(5gr), and at highest point v_top = √(gr).