Units and Dimensions Questions and Answers

Answer: C

A higher API number means a lighter oil, so the scale runs opposite to specific gravity. It is one of several industry scales, such as Baume and Twaddell, defined against water in the same way. Each was devised for a particular trade.

Answer: D

That invariance is exactly why such groups are used to correlate data, since a Reynolds number computed in imperial units matches one computed in SI. It also provides a check that the group has been assembled correctly.

Answer: A

It compares inertial with viscous forces and its four quantities combine to give a dimensionless ratio. The second grouping is the Prandtl number and the third relates to the Froude number. Its value decides whether flow is laminar or turbulent.

Answer: B

Correct answer: A-2, B-4, C-1, D-3

Each group is a ratio of two competing effects. Reynolds compares inertial with viscous forces and decides whether the flow is laminar or turbulent. Prandtl compares momentum with thermal diffusivity, so it says whether the velocity or the temperature boundary layer is thicker. Nusselt compares convective with conductive heat transfer at a surface. And Froude compares inertial with gravitational forces, which governs free surface and wave behaviour.

Answer: C

Both are true and the reason gives the mechanism: an experiment that would need five variables varied independently may reduce to two dimensionless groups, cutting the work by orders of magnitude. It also tells you how to scale a model to full size.

Answer: D

Six variables minus three dimensions gives three groups. The theorem gives the number rather than the form, and choosing which variables to repeat decides what those groups look like. Different choices give equally valid but different groups.

Answer: A

It counts molecules rather than weighing them, which is why stoichiometry works in moles. The molar mass and the molar volume are properties that connect the count to mass and volume respectively. Avogadro's number fixes how many entities a mole contains.

Answer: B

Correct answer: 2

\[ \frac{88\ \mathrm{g}}{44\ \mathrm{g/mol}} = 2\ \mathrm{mol}. \] Dividing mass by molar mass gives moles, and the units confirm it - grams over grams per mole leaves moles. Multiplying instead would give 3872 with the meaningless units of grams squared per mole.

Answer: C

The newton is a derived unit built from mass, length and time. Knowing which units are base and which derived is what makes a dimensional reduction possible in the first place. Seven base units cover the whole of the SI system.

Answer: D

The first two are correct. The third confuses precision with accuracy, since extra digits merely restate the uncertainty of the input data with a false appearance of confidence. The rule protects the reader from a spurious precision.