Question
Derive an expression for gravitational field strength due to the earth and show that it is equal to acceleration due to gravity at that point.
Solution
Consider the earth to be a homogenous sphere of mass M and radius R.
To find the gravitational field strength at a point P which is at a distance r from center of the earth, place the unit mass at that point.
The magnitude of the force on the unit mass is gravitational field strength at that point.
Gravitational field strength at a point is given by,
i.e.
...(1)
Also, acceleration due to gravity at point P is,
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...(2)
From (1) and (2), we get,
E = g
That is, the gravitational field strength due to the earth is equal to the acceleration due to gravity.
To find the gravitational field strength at a point P which is at a distance r from center of the earth, place the unit mass at that point.
The magnitude of the force on the unit mass is gravitational field strength at that point.
Gravitational field strength at a point is given by,
i.e.
...(1)Also, acceleration due to gravity at point P is,
...(2) From (1) and (2), we get,
E = g
That is, the gravitational field strength due to the earth is equal to the acceleration due to gravity.
