Dimensional Formula of Gravitational Constant

Question: What is the dimensional formula of the gravitational constant (G)?

  1. [M]^-1 [L]^3 [T]^-2
  2. [M] [L]^3 [T]^-2
  3. [M]^-1 [L]^2 [T]^-1
  4. [M] [L] [T]^-1

Answer: A) [M]^-1 [L]^3 [T]^-2

Solution: The dimensional formula of the gravitational constant, denoted as “G,” is an essential parameter in physics, used to describe the strength of the gravitational force between two objects. In the International System of Units (SI), the dimensional formula of G is represented as [M]^-1 [L]^3 [T]^-2.

Here’s a breakdown of the dimensions used in this formula:

  • [M] represents mass, which is measured in kilograms (kg).
  • [L] stands for length, which is typically measured in meters (m).
  • [T] denotes time, measured in seconds (s).

The formula [M]^-1 [L]^3 [T]^-2 signifies that the gravitational constant has units of kilograms to the power of negative one, meters cubed, per second squared. This dimensional formula allows scientists and engineers to incorporate G into various equations, such as Newton’s law of universal gravitation, which relates the gravitational force between two objects to their masses and the distance between them. Understanding the dimensional formula of G is fundamental to making accurate calculations in gravitational physics.

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