Question

how does the acceleration due to gravity change below the surface of the earth​

Answer 1

Answer:

To calculate acceleration due to gravity below the surface of the earth (between the surface and centre of the earth).

Density of the earth is constant throughout. Therefore,

ρ = Me / (4/3π Re3) equation(1)

where

Me = mass of the earth

Volume of sphere= 4/3π Re3

Re = radius of the earth.

As entire mass is concentrated at the centre of the earth.

Therefore density can be written as

ρ = Ms / (4/3π Rs3) equation (2)

Comparing equation (1) and (2)

Me/Ms = Re3/Rs3 where Rs = (Re-d) 3

d= distance of the body form the centre to the surface of the earth.

Therefore,

Me/Ms = Re3/(Re-d)3

Ms = Me(Re-d)3/Re3 from equation(3)

To calculate Gravitational force (F) between earth and point mass m at a depth d below the surface of the earth.