What will be the change in the value of ‘g’ if: (a) As one goes above the earth’s surface (b) Goes down towards the center of earth
Answers
Explanation:
Now in this unit, a second equation has been introduced for calculating the force of gravity with which an object is attracted to the earth.
where d represents the distance from the center of the object to the center of the earth.
In the first equation above, g is referred to as the acceleration of gravity. Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location. They also result from the fact that the earth is not truly spherical; the earth's surface is further from its center at the equator than it is at the poles. This would result in larger g values at the poles. As one proceeds further from earth's surface - say into a location of orbit about the earth - the value of g changes still.
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.
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.
The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. 5.98x1024 kg) and the distance (d) that an object is from the center of the earth. If the value 6.38x106 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/s2. 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 6.38x106 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/s2.
Answer:
Now in this unit, a second equation has been introduced for calculating the force of gravity with which an object is attracted to the earth.
where d represents the distance from the center of the object to the center of the earth.
In the first equation above, g is referred to as the acceleration of gravity. Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location. They also result from the fact that the earth is not truly spherical; the earth's surface is further from its center at the equator than it is at the poles. This would result in larger g values at the poles. As one proceeds further from earth's surface - say into a location of orbit about the earth - the value of g changes still.
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.
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.
The above equation demonstrates that the acceleration of gravity is dependent upon the mass of the earth (approx. 5.98x1024 kg) and the distance (d) that an object is from the center of the earth. If the value 6.38x106 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/s2. 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 6.38x106 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/s2.
As is evident from both the equation and the table 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.
As the depth increased the mass of the earth decreases. At the surface of earth this value will be maximum because radius will be maximum. When radius becomes less this value also decreases. Hence acceleration due to gravity decreases with increase in the depth.
Explanation: