Units and Dimensions Questions and Answers

Answer: A

Correct answer: a ratio equal to one, multiplying any expression

Since 1 metre and 100 centimetres are the same length, the ratio of one to the other is exactly one, and multiplying by it changes the value of nothing while changing the units of everything. Treating conversions this way makes them algebra rather than recollection: write the ratio the way round that cancels the unit you have, and the arithmetic follows.

Answer: B

Correct answer: 2 - 4 - 1 - 3

Write the quantity with its units, write each conversion factor as a ratio equal to one, cancel the units algebraically, and only then do the arithmetic. Doing the numbers first is what produces answers that are right in magnitude and wrong by a factor of sixty or a thousand, because the cancellation is the step that catches an inverted factor.

Answer: C

The pressure of a column is density times gravity times height, so thirteen thousand six hundred times nine point eight one times zero point seven six gives about one hundred and one thousand pascals. The chain of units cancels to pascals exactly.

Answer: D

One measures mass and the other force, and the conversion between them involves the acceleration due to gravity through the factor conventionally called g sub c. Confusing them is the classic hazard of the imperial system.

Answer: A

The pound mass and the pound force were both defined so that one weighs one under standard gravity, which forces a conversion constant into Newton's second law. In SI the newton is defined so that the constant is one and disappears.

Answer: B

The first two are correct. The third is false for an ideal gas, where equal volumes contain equal numbers of moles, so the two percentages coincide. That equality does not hold for liquids. Liquid volumes are not additive on mixing either.

Answer: C

Correct answer: a stated reference temperature and pressure

A normal cubic metre is a fixed quantity of gas, expressed as the volume it would occupy at a stated reference condition - commonly 0 degrees Celsius and one atmosphere, though the reference must always be checked since standard cubic metres and feet use others. Quoting a gas flow at actual line conditions would say nothing about how much gas was passing, which is precisely why the convention exists.

Answer: D

Mass is conserved and unaffected by conditions, whereas volume responds to both through the density. This is why material balances are written on a mass or mole basis rather than a volumetric one. A volumetric flow must always carry its conditions with it.