The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity. The recognition of concepts of dimensions, which guide the description of physical behaviour is of basic importance as only those physical quantities can be added or subtracted which have the same dimensions. A thorough understanding of dimensional analysis helps us in deducing certain relations among different physical quantities and checking the derivation, accuracy and dimensional consistency or homogeneity of various mathematical expressions. When magnitudes of two or more physical quantities are multiplied, their units should be treated in the same manner as ordinary algebraic symbols. We can cancel identical units in the numerator and denominator. The same is true for dimensions of a physical quantity. Similarly, physical quantities represented by symbols on both sides of a mathematical equation must have the same dimensions.
If speed v, acceleration A and force F , are considered as fundamental units, the dimension of Young’s modulus will be
Options:
(a) `[v^(-4)A^(-2)F]`
(b) `[v^(-2)A^2F^2]`
(c) `[v^(-2)A^2F^(-2)]`
(d) `[v^(-4)A^2F^1]`