Show that the acceleration due to gravity at the centre of the earth is zero.
Show that the acceleration due to gravity at the centre of the earth is zero.
Acceleration due to gravity of our earth varies at poles and equator due to the following reasons:
1. Rotation of the earth:
The centrifugal on any object on the earth depends on the distance of the object from the axis of rotation of the earth.
g/= g - ω2R
Any object at the equator is at the maximum distance from the axis. Whereas, an object at the pole will be near the axis. So, acceleration due to gravity is less at the equator than at the poles.
2. Non sphericity of the earth:
The radius in the equatorial plane is about 21 Km larger than the radius along the poles. The value of g is accordingly larger at poles and less at the equator.
Also the value of g inside the Earth is directly proportional to the distance from the Earth 's centre.
g’=g(1-2h/R)
Hence, g decreases as you go down into the Earth until it becomes zero at the centre of the Earth.
Acceleration due to gravity of our earth varies at poles and equator due to the following reasons:
1. Rotation of the earth:
The centrifugal on any object on the earth depends on the distance of the object from the axis of rotation of the earth.
g/= g - ω2R
Any object at the equator is at the maximum distance from the axis. Whereas, an object at the pole will be near the axis. So, acceleration due to gravity is less at the equator than at the poles.
2. Non sphericity of the earth:
The radius in the equatorial plane is about 21 Km larger than the radius along the poles. The value of g is accordingly larger at poles and less at the equator.
Also the value of g inside the Earth is directly proportional to the distance from the Earth 's centre.
g’=g(1-2h/R)
Hence, g decreases as you go down into the Earth until it becomes zero at the centre of the Earth.
