Which one of the following is NOT the unit of energy?
- (a)Joule
- (b)Watt-hr
- (c)Newton-metre
- (d)kg-metre/sec²
Correct — D, kg-metre/sec². The quantity kg x metre / second-squared is mass times acceleration, which by Newton's second law is force — that combination is the newton, a unit of force, not energy. The other three are all units of energy (or work), so kg-m/s squared is the one that is NOT energy.
- (a)Joule — The joule is the SI unit of energy and work (1 J = 1 newton-metre), so it is a unit of energy.
- (b)Watt-hr — A watt-hour is power (watt) multiplied by time (hour), which is energy; 1 watt-hour equals 3600 joules.
- (c)Newton-metre — A newton-metre is force times distance, which is work/energy and equals one joule (as a torque unit it shares the same dimensions).
Energy and work share the dimension force x distance, whose SI unit is the joule (newton-metre); power multiplied by time (watt-hour) is also energy. Force, by contrast, has the dimension mass x acceleration = kg x m/s squared = newton. Checking the dimensional make-up of each unit reveals which quantity it measures.
Every option looks 'physics-like', so the tell is to expand kg-m/s squared: that is mass times acceleration = newton = force, not energy. Force differs from energy by one factor of distance.
- Energy and work share the unit joule (a newton-metre), while a watt-hour (power times time) equals 3600 joules.
- The newton, equal to kg times m/s squared (mass times acceleration), is the unit of force.
- Because work equals force times distance, the joule equals a newton times a metre.
- kg-metre/second-squared is therefore a unit of force, not of energy.
kg-m/s² is a unit of force (the newton); the other three measure energy.
- Assuming any physics-looking unit is energy without expanding its dimensions.
- Confusing the newton-metre (energy/torque) with kg-m/s squared (force).
Asked as 'which is/is not a unit of X' — decode each unit to its base dimensions to classify it.
Match List I (Quantity) with List II (Units): I. High speed II. Wavelength III. Pressure IV. Energy; A) Mach B) Angstrom C) Pascal D) Joule.
- (a) I-B, II-A, III-C, IV-D
- (b) I-A, II-B, III-D, IV-C
- (c) I-A, II-B, III-C, IV-D
- (d) I-B, II-A, III-D, IV-C
Answer(c) I-A, II-B, III-C, IV-D
Same skill — matching units to the physical quantities they measure. UPSC 1999 pairs quantities with units (energy = joule); this NDA item asks which listed unit is NOT energy (the newton).
The universal constant of gravitation G has the unit
- (a) N
- (b) m/s
- (c) Joule
- (d) N-m²/kg²
Answer(d) N-m²/kg²
Same idea — reading physical quantities from their units. That NDA item derives the unit of G; this one classifies units as energy or force from their dimensions.
- practice — not a real PYQ
The combination kg x metre / second-squared is the SI unit of which quantity?
- (a)Energy
- (b)Power
- (c)Force
- (d)Pressure
Answer(c) Force — it equals the newton (mass times acceleration).
- practice — not a real PYQ
One kilowatt-hour of electrical energy is equal to
- (a)3.6 x 10^6 joules
- (b)1000 joules
- (c)3600 joules
- (d)60 joules
Answer(a) 3.6 x 10^6 joules — 1000 W x 3600 s.