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Physics For Scientists & Engineers
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Short Answer

Newton’s law of universal gravitation is represented by


whereF is the magnitude of the gravitational force exerted by one small object on another, M and are the masses of the objects, and r is a distance. Force has the SI units Kgm/s2 . What are the SI units of the proportionality constant role="math" localid="1663610883447" G?

The SI unit of the gravitational constant G is:


See the step by step solution

Step by Step Solution

Step 1: Analysis of given data

The formula of the Newton’s law of gravitation is F=GMmr2, where F is the gravitational force, M and m are the masses of bodies, and r is the distance between the bodies. ………..(1)

It has given that the dimension of force is kgm/s2.

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.

Step 2: Write the units of physical quantity

The unit of mass is kg

The unit of length is m

The unit of time is s

Step 3: Determination of units of gravitational constant  G

Rewrite the equation (1).


Write the SI units for the quantities in the above formula.


Rearrange the above equation for G and cancel the equal terms.


Hence, the SI unit of the gravitational constant G is:


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