Units and Measurements: SI Units, Dimensions and Instruments

The correct answer is B, newton. 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. Its dimensional formula is therefore M L T⁻².

Option A, the joule, is the unit of work and energy: one joule is the work done when a force of one newton moves its point of application through one metre. Option C, the watt, is the unit of power, that is the rate of doing work, and equals one joule per second. Option D, the pascal, is the unit of pressure and equals one newton per square metre. All four are derived units named after scientists, and papers often list them together to see whether you can match each with its quantity.

The correct answer is C, seven. 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. Every other unit in science is derived from these by multiplication and division.

Options A and B fall short of the list and usually come from forgetting the mole or the candela, which are the two least familiar. Option D, nine, comes from adding the radian and the steradian, the units of plane angle and solid angle; these were long treated as a separate class called supplementary units and are not counted among the base units. A safe way to remember the seven is by their quantities: length, mass, time, current, temperature, amount of substance and luminous intensity.

The correct answer is C, newton. 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. Derived units are always expressible in terms of the base units.

Option A, the kelvin, is the base unit of thermodynamic temperature. Option B, the mole, is the base unit for the amount of substance and contains as many entities as there are atoms in a fixed quantity of carbon-12 under the older definition. Option D, the candela, is the base unit of luminous intensity and is the one most often forgotten in the list. In this style of question the odd one out is almost always a unit named after a scientist, such as the newton, joule, watt, pascal or hertz.

The correct answer is A, luminous intensity, that is the brightness of a source of light in a given direction. 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.

Option B, electric current, is measured in ampere, named after the French scientist Andre-Marie Ampere. Option C, amount of substance, is measured in mole, which is the chemist's counting unit for atoms and molecules. Option D, pressure, is measured in pascal, a derived unit equal to one newton per square metre. Two related units are worth knowing alongside the candela: the lumen for luminous flux and the lux for illuminance, that is the light falling on a surface.

The correct answer is B, distance. 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. It is used for the enormous distances between stars, where kilometres would run to unmanageable numbers.

Option A is the trap built into the name; the word year refers to the time taken by the light, not to the quantity measured. Option C, speed, has its own units such as metres per second. Option D, brightness, is measured by other quantities altogether, such as magnitude in astronomy. Two more distance units belong with this one: the astronomical unit, the mean distance between the Earth and the Sun, and the parsec, which equals about 3.26 light years.

The correct answer is B, pascal. Pressure is force divided by area, so its unit is one newton per square metre, which is given the name pascal after Blaise Pascal. Its dimensional formula is M L⁻¹ T⁻², and atmospheric pressure at sea level is about 1.013 lakh pascals, also written as one atmosphere or about 1,013 millibars.

Option A, the newton, measures force itself and not force per unit area; this is the commonest confusion in the question. Option C, the hertz, measures frequency, that is the number of cycles per second. Option D, the tesla, measures magnetic flux density. Remember that the instrument used to measure atmospheric pressure is the barometer, and a sudden fall in its reading warns of a storm. Two other units of pressure are worth knowing: the bar, which is one lakh pascals, and the torr, the pressure of one millimetre of mercury.

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.

The correct answer is B, barometer. A barometer measures the pressure of the atmosphere, traditionally by balancing it against a column of mercury. It is also used for forecasting weather, because a sudden drop in pressure signals an approaching storm, and for finding altitude, since pressure falls as one rises.

Option A, the hygrometer, measures the humidity of the air. Option C, the anemometer, measures the speed of the wind and is the cup-shaped device seen at weather stations. Option D, the lactometer, checks whether milk has been diluted, by measuring its relative density. Keep the confusing pair apart: hygrometer for humidity and hydrometer for the density of a liquid. The mercury barometer was invented by Evangelista Torricelli, and the aneroid barometer, which uses a sealed metal box instead of a liquid, is the portable form carried on aircraft and used as an altimeter. Pressure itself is measured in pascals, and one atmosphere is about 1.013 lakh pascals.

The correct answer is B, amount of substance. The mole is the chemist's counting unit: one mole of any substance contains the Avogadro number of particles, about six followed by twenty-three zeros, whether those particles are atoms, molecules or ions. It is one of the seven base units of the SI system and is written with the symbol mol.

Option A, mass, has the kilogram as its base unit; the two are related through molar mass but are not the same quantity. Option C, density, is a derived quantity measured in kilograms per cubic metre. Option D, volume, is also derived and is measured in cubic metres, with the litre used as a convenient practical unit. Questions of this type test the pairing of each base unit with its own quantity, so learn all seven pairs together.

The correct answer is B, 746 watts. The horsepower is an older practical unit of power that survives in the rating of engines, pumps and motors, and it equals about 746 watts. The watt itself is the SI unit of power and means one joule of work done in one second.

Option A, 500 watts, and Option D, 1,200 watts, correspond to no standard unit. Option C, 1,000 watts, is one kilowatt, which is a different and very common unit: the electricity used at home is billed in kilowatt hours, popularly called units, where one kilowatt hour is the energy used by a one kilowatt appliance running for one hour. Keep the two apart, since a question often offers the kilowatt as a distractor for horsepower.

The correct answer is B, lactometer. A lactometer floats in milk and shows its relative density. Pure milk is denser than water, so adding water lowers the density and the instrument sinks deeper, which reveals the adulteration. It is in effect a hydrometer calibrated for one particular liquid.

Option A, the hydrometer, measures the relative density of liquids in general, so it is the parent instrument rather than the specific answer this question wants. Option C, the pyrometer, measures very high temperatures, such as those inside a furnace, without touching the hot body. Option D, the fathometer, measures the depth of the sea using sound waves. Instrument questions are pure pairing questions, so revise them as a table rather than one at a time. A lactometer is therefore read where its stem meets the surface of the milk, and a reading below the pure-milk mark points to added water.