Question

How can we determine that the value of 'g' is 9.8?​

Answer 1

Answer:

The Value of g Depends on Location

To understand why the value of g is so location dependent, we will use the two equations above to derive an equation for the value of g. First, both expressions for the force of gravity are set equal to each other.

$m*g=\frac{G+M_{Earth+}m }{d^{2} }$

Now observe that the mass of the object - m - is present on both sides of the equal sign. Thus, m can be canceled from the equation. This leaves us with an equation for the acceleration of gravity.

$g=\frac{G+M_{earth} }{d^{2} }$

The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. 5.98x10^24 kg) and the distance (d) that an object is from the center of the earth. If the value 6.38x10^6 m (a typical earth radius value) is used for the distance from Earth's center, then g will be calculated to be 9.8 m/s^2. And of course, the value of g will change as an object is moved further from Earth's center. For instance, if an object were moved to a location that is two earth-radii from the center of the earth - that is, two times 6.38x10^6 m - then a significantly different value of g will be found. As shown below, at twice the distance from the center of the earth, the value of g becomes 2.45 m/s^2.

See the Picture Attached :)

As is evident from both the equation above, the value of g varies inversely with the distance from the center of the earth. In fact, the variation in g with distance follows an inverse square law where g is inversely proportional to the distance from earth's center. This inverse square relationship means that as the distance is doubled, the value of g decreases by a factor of 4. As the distance is tripled, the value of g decreases by a factor of 9. And so on. This inverse square relationship is depicted in the graph... Check the attachment :)

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