The dimensional formula of work is
- A.M L T⁻²
- B.M L² T⁻²
- C.M L² T⁻³
- D.M L⁻¹ T⁻²
Correct answer
Explanation
The correct answer is B, M L² T⁻². Work is force multiplied by displacement. Force has the dimensions M L T⁻², and multiplying it by a length adds one more power of L, which gives M L² T⁻². Energy has the same dimensions as work, since energy is the capacity to do work, and so does torque.
Option A, M L T⁻², is the dimensional formula of force, and also of weight, which is a force. Option C, M L² T⁻³, belongs to power, since power is work divided by time and therefore carries one extra power of T in the denominator. Option D, M L⁻¹ T⁻², is the formula for pressure, which is force divided by area. Because work and torque share the same dimensions, dimensional analysis alone cannot tell them apart, a standard limitation of the method.
Read the full article: Units and Measurements: SI Units, Dimensions and Instruments
Practice Questions
View allWhat is the SI unit of force?
- A.Joule
- B.Newton
- C.Watt
- D.Pascal
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One newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared, which follows directly from the equation force equals mass times acceleration.
Read the full explanation →How many base units are there in the International System of Units (SI)?
- A.Five
- B.Six
- C.Seven
- D.Nine
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The SI system, adopted in 1960 by the General Conference on Weights and Measures, rests on seven base units: the metre, the kilogram, the second, the ampere, the kelvin, the mole and the candela.
Read the full explanation →Which one of the following is NOT a base unit of the SI system?
- A.Kelvin
- B.Mole
- C.Newton
- D.Candela
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The newton is a derived unit: it is built from the kilogram, the metre and the second, since force equals mass times acceleration, and it can be written as one kilogram metre per second squared.
Read the full explanation →The candela is the SI unit of which physical quantity?
- A.Luminous intensity
- B.Electric current
- C.Amount of substance
- D.Pressure
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The candela takes its name from the candle, which was once used as a rough standard of light, and it is one of the seven base units of the SI system.
Read the full explanation →A light year is a unit of which of the following?
- A.Time
- B.Distance
- C.Speed
- D.Brightness of a star
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A light year is the distance that light, moving at about three lakh kilometres per second, covers in one year, which works out to roughly 9.46 trillion kilometres.
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