Work, Power, Energy — Physics

Q.1

WBCS Prelims 2021

A heavy body and a light body have equal kinetic energy. Then

A. heavy body has greater momentum.

B. light body has greater momentum.

C. both have equal momentum.

D. both have the same angular momentum.

Explanation

Core Formula/Logic: Kinetic energy KE = (1/2)mv2, momentum p = mv. For equal KE, p = sqrt(2m*KE), so momentum is proportional to sqrt(m).
Step-by-Step Solution: 1. Let m1 > m2, KE1 = KE2 = KE. 2. p1 = sqrt(2m1*KE), p2 = sqrt(2m2*KE). 3. Since m1 > m2, sqrt(m1) > sqrt(m2), therefore p1 > p2.
Common Pitfall: Incorrectly using p = sqrt(2KE/m) gives p proportional to 1/sqrt(m), making the light body appear to have greater momentum and leading to option B.
Shortcut/Takeaway: For equal kinetic energy, momentum ∝ sqrt(mass). The heavier body always has greater momentum. Direct formula: p = sqrt(2mKE).

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Q.2

WBCS Prelims 2007

When a body is lifted by hand, what type of work is performed by hand?

A. First type of lever

B. Second type of lever

C. Third type lever

D. Simple machine

Explanation

Why Correct: Lifting a body by hand uses the forearm as a third-class lever where the effort (hand muscles) lies between the fulcrum (elbow joint) and load (weight being lifted), maximizing speed and range of motion.
Distractor Analysis: First-class levers place the fulcrum between effort and load (like scissors). Second-class levers place the load between fulcrum and effort (like a wheelbarrow). 'Simple machine' is a broad category that includes levers but is too general for this specific mechanism.
Takeaway: Human body contains all three lever classes: neck nodding is first-class, standing on toes is second-class, and most limb movements (biceps curl, throwing) are third-class.

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Q.3

WBCS Prelims 2006

What kind of energy works when a watch spring is wound up?

A. Kinetic energy

B. Potential energy

C. Electrical energy

D. Magnetic energy

Explanation

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.

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Q.4

WBCS Prelims 2004

A raindrop falls with a uniform velocity

A. its potential energy remains constant

B. its mechanical energy is constant

C. its mechanical energy is transferred of the atmosphere

D. the total energy of the drop

Explanation

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.

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