Question

Which definition is correct and uses only quantities and not units?
A) Density is mass per cubic meter.
B) Potential difference is energy per unit current.
C) Pressure is force per unit area.
D) Speed is distance travelled per second.

Answer 1

Hint: The question specifies quantities and not units meaning, the definition has variables that have their own definition and are composed of other units whereas units are standards of measurement of physical quantities or objects. Let us see which options have units and which have values that can be further simplified into units.

Complete step by step solution:
Let us check the options one by one, the first option is density is mass per cubic meter, the formula for density is mass per unit volume here instead of volume a unit of volume that is cubic meter is given hence, wrong as there are many other units of volume than cubic meter.
The second option, potential difference is energy per unit current is false as potential difference is energy per unit charge (q) which is current (i) upon time (t) charge is flowing.

The definition can be formulated as:
Potential Difference (P.E.) = $\dfrac{E}{q}$ with $q=\dfrac{i}{t}$.
The third option, Pressure is force per unit area is current as both force and area are quantities and the definition is true as well meaning, if formulated then the formula is:
\[P=\dfrac{F}{A}\]
The last option is half true as second is unit and not quantity; time is quantity.

Therefore, the correct answer is pressure is force per unit area.

Note: Option (A) and (D) are true in definition but not entirely as volume can be $m^3$, $km^3$, $mm^3$, litre etc. and the same goes for option D as time can be seconds, minutes, hours etc.