Why Correct: Winding a watch spring stores elastic potential energy by deforming the spring material, which gets converted to kinetic energy as it unwinds to power the watch mechanism.
Distractor Analysis: Kinetic energy involves motion of objects, electrical energy involves flow of electric charge, and magnetic energy involves magnetic fields and forces.
Takeaway: In physics, potential energy includes gravitational, elastic, chemical, and nuclear forms - elastic potential energy follows Hooke's Law where stored energy equals 1/2kx2.

Core Formula/Logic: Mechanical energy = Potential energy + Kinetic energy. At uniform velocity, kinetic energy is constant but potential energy decreases with height.
Step-by-Step Solution: 1. Uniform velocity means zero net force and constant kinetic energy (KE = 1/2 mv2).
2. As height decreases, potential energy (PE = mgh) decreases continuously.
3. Total mechanical energy (PE + KE) decreases because PE decreases while KE remains constant.
4. The lost mechanical energy converts to thermal energy in the atmosphere through air resistance.
Common Pitfall: Assuming constant velocity means constant mechanical energy ignores potential energy decrease. Thinking total energy decays violates energy conservation - energy transfers but doesn't disappear.
Shortcut/Takeaway: For objects falling at terminal velocity, mechanical energy decreases linearly with height, with energy loss equal to work done against air resistance.

Why Correct: The SI unit of power is the watt (W), defined as one joule per second (1 W = 1 J/s). Power is the rate of doing work or transferring energy.
Distractor Analysis: Half-life is a time measure in radioactive decay, not a power unit. Volt (V) is the unit of electric potential or emf. Joule (J) is the unit of energy or work, not power.
Takeaway: Power = Work/Time. Memorize: 1 Watt = 1 J/s. Common derived SI units: watt (power), volt (potential), joule (energy).

Why Correct: Two 60 W bulbs consume 120 W total. Operating 5 hours daily for 10 days gives 50 hours of use. Energy consumed = 0.12 kW × 50 h = 6 kWh. At Rs. 3.50 per kWh, total cost = 6 × 3.50 = Rs. 21.00.
Distractor Analysis: Rs. 10.50 results from using only one bulb or half the time. Rs. 38.50 corresponds to 11 kWh consumption. Rs. 77.00 corresponds to 22 kWh consumption.
Takeaway: Power consumed in kilowatts multiplied by time in hours gives energy in kilowatt-hours. Always convert watts to kilowatts by dividing by 1000.

Why Correct: For a body thrown vertically upwards, the total mechanical energy (sum of kinetic and potential energy) remains constant throughout the motion if air resistance is neglected. At the highest point, kinetic energy is zero but potential energy is maximum; total energy equals the initial kinetic energy.
Distractor Analysis: Great at the highest point would be true for potential energy only, not total energy. Lowest at the highest point would be true for kinetic energy. Greatest at any point is not accurate as total energy is invariant.
Takeaway: Conservation of mechanical energy: total energy = KE + PE = constant for free fall under gravity (no friction).

Core Formula/Logic: Kinetic energy KE = p^2/(2m), where p is momentum. If KE1 = KE2, then p1^2/(2m1) = p2^2/(2m2) -> p1/p2 = sqrt(m1/m2).
Step-by-Step Solution:
1. KE = p^2/(2m). Set KE1 = KE2: p1^2/(2m1) = p2^2/(2m2).
2. Cancel 2: p1^2/m1 = p2^2/m2.
3. Cross-multiply: p1^2 * m2 = p2^2 * m1.
4. Divide by p2^2 * m2: (p1/p2)^2 = m1/m2.
5. Take square root: p1/p2 = sqrt(m1)/sqrt(m2) = √m1 : √m2.
Common Pitfall: Choosing m1:m2 (option A) would be true if velocities were equal, not KE. Option C (m1^2:m2^2) confuses squaring when it should be square root. Option B reverses the ratio.
Shortcut/Takeaway: For equal KE, momentum is proportional to the square root of mass. Memorize: p ∝ √m when KE is constant. Example: if m1=4m2, then p1=2p2.

Why Correct: The gravitational force F acts radially inward toward the sun, while the planet's displacement over any arc of the circular orbit is tangential to the circle. Work done equals F × displacement × cos(θ), where θ is the angle between force and displacement. Here θ = 90° throughout the motion, and cos(90°) = 0, so the work done over half the circumference is zero.
Distractor Analysis: F × 2πr represents the work if the force acted along the full circumference in the direction of motion, which would apply to a tangential force, not a radial gravitational pull. F × πr corresponds to the work for half the circumference under the same incorrect tangential-force assumption. F × 2r equals the force multiplied by the diameter, which would apply if the force acted along a straight radial path of length 2r, but the planet moves along the curved orbit, not radially.
Takeaway: For any circular orbit under a central force like gravity, the work done over a complete revolution is also zero because the force remains perpendicular to the displacement at every instant. This principle extends to uniform circular motion generally, where centripetal forces do no work.