Question

Which of the following is not a derived unit?
A. Weight of a cube
B. Volume of a cube
C. Area of cube
D. Height of a cube

Answer 1

Basic concept of decimal units is to be used to find this answer. As derived units can be expressed in terms of fundamental quantities.

Complete step by step answer:
There are basically two types of quantities
1. Fundamental quantities: These are independent and cannot be defined in terms of other physical quantities.
There are $7$ basic quantities.
i.e.
1. Length
2. Mass
3. Time
4. Temperature
5. Electric current
6. Luminous intensity
7. Quantity of matter
Derived quantity: These art hos which can be expressed in terms of fundamental quantities by means of mathematical multiplication and division.
A weight of cube $= mass \times gravity$
Here we know gravity is a derived quantity and also weight is expressed in terms of mass and gravity. So, it is a derived unit.
B. Volume of cube $= length \times breadth \times height$
So, it is also expressed in terms of fundamental quantity as multiplication. So, it is also a derived quantity.
C. Area of cube $= length \times breadth$ is also expressed by multiplication operation of fundamental quantities length and breadth. So, it is also a derived unit.
D. Height of the cube is a length which is a fundamental quantity. Hence, height is not a derived unit.
Hence, the correction option is D.

Note: Derived quantities cannot be expressed in terms of addition or subtraction of fundamental units.Addition or subtraction of fundamental units leads to fundamental units again. For example$1$ metre$+ \,\,1\,metre = 2 metre$Length $+$ Length $=$ length.