Newton’s law of universal gravitation is represented by
whereF is the magnitude of the gravitational force exerted by one small object on another, and are the masses of the objects, and is a distance. Force has the SI units . What are the SI units of the proportionality constant role="math" localid="1663610883447" ?
The SI unit of the gravitational constant is:
The formula of the Newton’s law of gravitation is where is the gravitational force, and are the masses of bodies, and is the distance between the bodies. ………..(1)
It has given that the dimension of force is
The analysis of a relationship between different physical quantities by using the units of measurements and dimensions is called dimensional analysis. It is used to examine the correctness of an equation.
The unit of mass is
The unit of length is
The unit of time is
Rewrite the equation (1).
Write the SI units for the quantities in the above formula.
Rearrange the above equation for and cancel the equal terms.
Hence, the SI unit of the gravitational constant is:
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