Question

using the newton's law show that the value of 'g' decreases as one goes above the earth's surface

Answer 1

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This can easily be answer from the study material.

Newton's Law of Gravitation:



Let two objects I and II, of masses M1 and M2 respectively, be placed at a distance d from each other. As per the law of gravitation, the following two assertions can be made about the force of gravity (F) between the two objects.

 



Where, G is a constant called Universal Gravitational Constant or Newton’s constant.

Now, 

Let us consider a stone of mass m, dropped from a tower of height h. The stone will fall towards Earth’s surface having the mass M and radius R. This motion of the stone is called a free fall under the influence of Earth’s gravity.

Free fall is the motion of an object falling solely under the influence of Earth’s gravity.

Using Newton’s second law of motion, the force on the stone can be given by the product of its mass and acceleration.

F = ma

Suppose the stone falls freely with an acceleration g.

F = mg…(i)

Force exerted by Earth on the stone is given by Newton’s law of gravitation:

F = G

From equations (i) and (ii), we obtain:

mg = G

Or, g =

The height h is very small compared to Earth’s radius R. Hence, the term will be very small and can be neglected. So, we get:



Where,

G = Universal gravitational constant = 6.67 × 10?11 Nm2/kg2

M = Earth’s mass

R =Earth’s radius

This equation expresses the value of the acceleration due to gravity of an object placed on Earth’s surface. This value decreases as we move away from Earth’s surface or go below it. 

Earth’s radius R increases when we go from the poles to the equator. Consequently, the value of g decreases.