Qno 15 discuss the variation of g with depth . Derive the expression for it. What is the value of g at the centre of the earth
Dear student,
Consider 'ρ' be the density of the material of the earth so
mass=volume×density
M =ρ
Now substituting in equation (1)
g = πGRρ −−−−−−−−−−−(2)
Now, Consider the body be taken to the depth d below the surface of the earth.Then, the acceleration due to gravity at the depth below the surface of the earth is
gd = πG(R−d)ρ −−−−−−−−−(3)
Now, divide equation (3) by (2)
=
g = gd
This is an expression for the acceleration due to gravity at the depth below the surface of the earth and this expression shows the acceleration due to gravity decrease as we move down into the earth.
At the center of the earth d=R.
Hence, Acceleration due to gravity at the center of the earth is 0
Regards
The acceleration due to gravity on the surface of the earth is
g = −−−−−−−−−−−−−−−−(1)Consider 'ρ' be the density of the material of the earth so
mass=volume×density
M =ρ
Now substituting in equation (1)
g = πGRρ −−−−−−−−−−−(2)
Now, Consider the body be taken to the depth d below the surface of the earth.Then, the acceleration due to gravity at the depth below the surface of the earth is
gd = πG(R−d)ρ −−−−−−−−−(3)
Now, divide equation (3) by (2)
=
g = gd
This is an expression for the acceleration due to gravity at the depth below the surface of the earth and this expression shows the acceleration due to gravity decrease as we move down into the earth.
At the center of the earth d=R.
Hence, Acceleration due to gravity at the center of the earth is 0
Regards
