If the speed of light (c), acceleration due to gravity (g)...

If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as fundamental units, the dimensional formula of gravitational constant $(G)$ will be
(A) $c^{0} g p^{-3}$
(B) $c^{2} g^{3} p^{-2}$
(C) $c^{0} g^{2} p^{-1}$
(D) $c^{2} g^{2} p^{-2}$

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Key Concepts

Gravitational Constant

The gravitational constant, often denoted as G, is a proportionality factor in Newton's law of gravitation. When expressing G in terms of a non-standard set of fundamental units, it is necessary to determine the correct powers of these units so that the dimensions on both sides of the gravitational equation remain consistent.

Dimensional Analysis

Dimensional analysis is a technique used to express physical quantities in terms of fundamental dimensions. It is fundamental in physics for checking the consistency of equations and understanding how different physical quantities relate to each other when expressed using various sets of base units.

Fundamental Units

Fundamental units are the basic building blocks from which other units are derived. In many systems, choices like mass, length, and time are common, but alternative sets (such as the speed of light, gravitational acceleration, and pressure) can also serve as a basis. The choice of fundamental units affects the expression of derived constants.

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