PYQ Analysis Work, Energy & Power

10-Year Weightage

How Much Does WEP Matter?

CBSE BOARDS

~10 marks out of 120 in theory + numericals

NEET

~2-3 questions every paper. 0 years missed.

JEE MAIN

~2 questions per paper. High consistency.

JEE ADVANCED

~2-3 questions. Often multi-concept.

Topic-wise Frequency (NEET, 2014–2024)

Work-Energy Theorem34%

Conservation of Energy28%

Power18%

Spring Potential Energy12%

Work by Variable Force8%

Topic-wise Frequency (JEE Main, 2014–2024)

Work-Energy Theorem28%

Spring Systems & Energy22%

Vertical Circular Motion20%

Power (P = Fv)16%

F-x Graph / Variable Force14%

CBSE tests: Definitions (1–2 marks), derivations (3 marks), numericals (3–5 marks). Formula derivations have appeared in consecutive years. Know Work-Energy Theorem derivation and spring PE derivation.

2024 CBSE Board Derivation

Derive an expression for the kinetic energy of a particle of mass m moving with velocity v. Hence state the work-energy theorem. (3 marks)

💡 Analysis: Standard derivation using F = ma and kinematics. Appeared 4 times in last 10 years. Learn to write: Step 1 (F=ma), Step 2 (W=mas), Step 3 (as = v²−u²/2), Step 4 (W = ½mv²−½mu²). This exact sequence gets full marks.

2023 CBSE Board Numerical

A body of mass 5 kg is moving with a velocity of 2 m/s. If a force of 20 N acts on it in the direction of motion for 4 s, find the work done by the force. (3 marks)

💡 Analysis: W = ΔKE. First find final velocity using v = u + at = 2 + (20/5)×4 = 18 m/s. Then W = ½×5×18² − ½×5×2² = 810 − 10 = 800 J. Alternatively W = F×s where s = ut + ½at² = 40 m → W = 20×40 = 800 J.

2022 CBSE Board Conceptual

A person carrying a load on his head and moving on a horizontal road does no work. Justify this statement. (2 marks)

💡 Analysis: Force (normal/weight) is vertical. Displacement is horizontal. θ = 90°. W = Fd cos 90° = 0. This question appears almost every 2 years in CBSE. Know the justification clearly.

2021 CBSE Board Numerical

A pump is required to lift 600 kg of water per minute from a well 25 m deep. Calculate the power required. (g = 10 m/s²) (3 marks)

💡 Analysis: W = mgh = 600×10×25 = 150,000 J. t = 60 s. P = W/t = 2500 W = 2.5 kW. Classic pump problem — appears every other year. Key: convert minutes to seconds.

2020 CBSE Board Definition + Application

Define the term 'conservative force'. Give two examples. How does the potential energy of a spring vary with its displacement from equilibrium? (5 marks)

💡 Analysis: 5-mark question. Part 1: conservative force definition (path-independent). Part 2: Gravity, spring force as examples. Part 3: PE = ½kx² — parabolic variation. Draw the parabola graph to score full marks.

NEET WEP questions: 60% are direct formula or conceptual. 40% involve 2-step energy conservation. Rarely gets beyond 3 steps. Vertical circular motion minimum speed appears almost every 2 years.

NEET 2024 NEET UG WET

A body of mass 1 kg begins to move under the action of a time-dependent force F = (2tî + 3t²ĵ) N. What power developed by the force at time t = 2 s?

💡 Answer: P = F⃗·v⃗. First find velocity: F = ma → a = F/m = (2tî + 3t²ĵ). v = ∫a dt = (t²î + t³ĵ). At t=2: v = (4î + 8ĵ), F = (4î + 12ĵ). P = 4×4 + 12×8 = 16 + 96 = 112 W.

NEET 2023 NEET UG Circular Motion

A stone tied to a string of length L is whirled in a vertical circle with the other end at the center. At a certain instant of time, the stone is at its lowest position and has a speed u. Find the magnitude of the change in its velocity as it reaches the topmost position.

💡 Analysis: Speed at top using energy: v² = u² − 4gL. Change in velocity magnitude = u(top) − u(bottom) requires vector subtraction (both vertical, opposite directions): |Δv| = u + v = u + √(u²−4gL). This is a conceptual trap — direction matters.

NEET 2022 NEET UG Spring Energy

A spring of spring constant 5×10³ N/m is stretched initially by 5 cm from the unstretched position. The work required to stretch it further by another 5 cm is:

💡 Answer: W = ½k(x₂² − x₁²) = ½×5×10³×(0.1² − 0.05²) = ½×5000×(0.01−0.0025) = ½×5000×0.0075 = 18.75 J. This is the type where students mistakenly use W = ½k(0.05)² = 6.25 J. Wrong — it's the incremental work from x₁=5cm to x₂=10cm.

NEET 2019 NEET UG Momentum & KE

Two masses M and m (M > m) are given the same kinetic energy. The ratio of their velocities is:

💡 Analysis: Same KE: ½Mv₁² = ½mv₂² → v₁/v₂ = √(m/M). Since M > m, v₁ < v₂. Lighter mass moves faster for same KE. Answer: √(m/M) (less than 1). This exact concept appeared in 2015, 2017, 2019, 2022 — be alert.

JEE Main pattern: ~2 questions per paper, usually 1 numerical and 1 MCQ. Spring-mass + rough surface combinations dominate. F-x graph area problems appear 3–4 times per decade.

JEE Main 2024 JEE Main Spring + Friction

A block of mass 2 kg slides on a smooth surface with velocity 4 m/s and hits a spring of spring constant k = 100 N/m. If the block compresses the spring by 0.4 m before coming to rest, the surface must not have been smooth for the last ______ m. Find friction coefficient. (g = 10 m/s²)

💡 Analysis: ½mv² = ½kx² + μmgd (rough part d). 0.5×2×16 = 0.5×100×0.16 + μ×2×10×d. 16 = 8 + 20μd. Solve with assumption d = x = 0.4: 16 = 8 + 20×μ×0.4 → μ = 1. This is a "find μ" reverse problem — rare and high-difficulty.

JEE Main 2023 (Jan) JEE Main F-x Graph

The variation of force F with position x is shown in the graph. The work done by this force when the body moves from x = 0 to x = 6 m is: [Graph shows: F = 5N from 0–2m, then F changes linearly from 5N to −3N from 2–6m]

💡 Solution: W = Area(0 to 2) + Area(2 to 6). Area 1 = 5×2 = 10 J. Area 2 = ½(5+−3)×4 = ½×2×4 = 4 J. W_total = 14 J. Key skill: calculate trapezoid/triangle area with sign from graph. This graph type appears every 2–3 years.

JEE Main 2022 JEE Main Power + Efficiency

A machine gun fires 300 bullets per minute. Each bullet of mass 10 g travels with a velocity of 600 m/s. The power of the machine gun is:

💡 Solution: KE of one bullet = ½×0.01×600² = 1800 J. Bullets per second = 300/60 = 5. Power = KE per second = 5×1800 = 9000 W = 9 kW. Classic power-as-rate-of-energy problem. Appears frequently.

JEE Main 2021 JEE Main Vertical Loop

A ball of mass 0.5 kg is attached to a string of length 0.5 m. Find the minimum speed at the lowest point of vertical circular motion for the ball to complete the circle.

💡 Solution: v_min(bottom) = √(5gR) = √(5×10×0.5) = √25 = 5 m/s. Direct formula. But JEE Main often asks for tension at bottom too: T = 6mg = 6×0.5×10 = 30 N. Know both results.

JEE Advanced: Multi-concept problems. PE curves, variable forces, non-inertial frame energy, spring system with friction in 3D. Rarely standalone WEP — almost always combined with another chapter. Always multi-correct MCQ.

JEE Adv 2023 JEE Advanced PE Curve Analysis

A particle of mass 1 kg is placed at a point x = 0, where potential energy is given as U(x) = 3x⁴ − 16x³ + 24x² − 10. Which of the following are correct? [Multi-correct question about equilibrium points, stability, force at specific points]

💡 Analysis: Find dU/dx = 0 → 12x³ − 48x² + 48x = 0 → 12x(x² − 4x + 4) = 0 → x = 0 or x = 2 (double root). At x=0: d²U/dx² = 48 > 0 (stable). At x=2: d²U/dx² = 0 (neutral/inflection). Force at any x: F = −dU/dx.

JEE Adv 2021 JEE Advanced Rolling + Energy

A solid cylinder of radius R rolls on a curved surface (quarter circle of radius 2R) from the top. Find the speed of the cylinder when it reaches the bottom. The cylinder does not slip at any point.

💡 Analysis: Height fallen = 2R − R = R (center of mass falls by R only, since cylinder has radius R). Energy: MgR = ½Mv² + ½(MR²/2)(v/R)² = ½Mv² + ¼Mv² = ¾Mv². v = √(4gR/3). This is a trap — height of center of mass ≠ radius of circular track.

JEE Adv 2019 JEE Advanced Spring Ladder Problem

Two blocks A (2 kg) and B (2 kg) are connected by a spring. Block A rests on a frictionless surface. B is placed on A. The system is compressed by 0.1 m and released. Find the separation when spring returns to natural length. (k = 100 N/m)

💡 Analysis: Use momentum conservation (system initially at rest → total momentum = 0 always). At natural length: p_A = −p_B → m_A v_A = m_B v_B → v_A = −v_B. Then energy: ½kx² = ½m_A v_A² + ½m_B v_B² → v_A = v_B = 0.5 m/s. This is a two-body spring problem — JEE Advanced standard.

Pattern Analysis — What to Expect Next

🔴 Repeated Every Year (Never Skip)

Work-Energy Theorem (All exams) ▾

Type: Find final velocity given work done by multiple forces. CBSE: 2-step. NEET: 3-step. JEE: 4-step with incline + spring + friction.

If you see F, d, v, m in the same problem → WET is the approach. Always.

KE = p²/2m relationship ▾

NEET tests this almost every 2 years: "Same KE — which has more momentum?" or "Same momentum — which has more KE?" Answer: use KE = p²/2m systematically.

Power = P = Fv at constant speed ▾

JEE Main: Vehicle/motor problems at constant velocity. At constant speed: F_engine = F_friction. P = f×v. The "efficiency" variant: P_useful = η × P_input.

🟡 Appears 3–5 Times Per Decade

Vertical circular motion minimum speed ▾

NEET + JEE Main: v_min at bottom = √(5gR). String vs rod vs track: different conditions. String: N = 0 at top → v_top = √(gR). Rod: can push → v_top = 0 is minimum. Track: same as string unless otherwise stated.

Spring PE increment problem ▾

W = ½k(x₂² − x₁²) when stretched from x₁ to x₂. Traps: Using ½k(x₂−x₁)² which is WRONG. Use ½k(x₂²−x₁²) every time.

½k(Δx)² ≠ ΔPE. The correct formula is ½k(x₂²−x₁²).

PE curve equilibrium analysis (JEE Adv) ▾

Given U(x) function: find equilibrium points, determine stability, find force at a point, find turning points for given total energy. This is a guaranteed multi-correct question in JEE Advanced every 3–4 years.

Prediction for next exam: Based on 10-year analysis — expect a spring + rough surface numerical in JEE Main, a "same KE momentum comparison" in NEET, and a PE curve multi-correct in JEE Advanced. These have 5-year cycles and are due.

Difficulty Trend (2014–2024)

Year	CBSE Difficulty	NEET Difficulty	JEE Main Difficulty	JEE Adv Difficulty
2024	⭐⭐ Moderate	⭐⭐⭐ High	⭐⭐⭐ High	⭐⭐⭐⭐ Very High
2023	⭐⭐ Moderate	⭐⭐ Moderate	⭐⭐⭐ High	⭐⭐⭐⭐⭐ Extreme
2022	⭐ Easy	⭐⭐ Moderate	⭐⭐⭐ High	⭐⭐⭐⭐ Very High
2021	⭐⭐ Moderate	⭐⭐ Moderate	⭐⭐ Moderate	⭐⭐⭐⭐ Very High
2020	⭐ Easy	⭐⭐ Moderate	⭐⭐⭐ High	⭐⭐⭐ High
2019	⭐⭐ Moderate	⭐⭐⭐ High	⭐⭐⭐ High	⭐⭐⭐⭐⭐ Extreme
2018	⭐ Easy	⭐ Easy	⭐⭐ Moderate	⭐⭐⭐⭐ Very High