Question

Which of the following is incorrect?
A. All derived quantities may be represented dimensionally in terms of the base quantities.
B. A base quantity cannot be represented dimensionally in terms of base quantities.
C. The dimension of a derived quantity is never zero in any base quantity.
D. The dimension of a base quantity in other base quantities is always zero.

Answer 1

Hint: We have certain physical quantities in nature which cannot be expressed in terms of other quantities known as base quantities. We can use these quantities in combination with other base quantities to derive new physical quantities.

Complete step-by-step answer:
Base quantities can be defined as the fundamental quantities from which other physical quantities can be derived. The quantities which are derived from the base quantities are known as the derived quantities.
Let us consider all the options one by one.
A. All derived quantities may be represented dimensionally in terms of the base quantities.
This statement is true based on the definition of the derived quantities.
B. A base quantity cannot be represented dimensionally in terms of base quantities.
This statement is also true as the base quantities are independent of the other base quantities.
C. The dimension of a derived quantity is never zero in any base quantity.
This statement is incorrect because derived quantities may have zero dimensions in certain base quantities. For example, acceleration, which is a derived quantity, has zero dimensions in the mass, which is a base quantity.
D. The dimension of a base quantity in other base quantities is always zero.
This is also correct as the statement is a direct consequence of option B.
Hence, the incorrect statement is option C.

Note: The dimensions of a physical quantity tell us how that quantity depends on the various base quantities or the fundamental quantities. There are seven base quantities in nature. All the physical quantities in nature can be expressed in terms of these seven fundamental quantities.