# Derivation of acceleration due to gravity1)at an altitude2)at a depth inside the earth

2
by priyasuniabha
do u need the value only

## Answers

• Brainly User
2015-10-31T10:38:03+05:30
F1=m1g                                      ............................................ accelaration due to gravity
F2=GM1 M2/R²
F= gravitational force
g= gravitational accelaration
R= distance means height
both shows force so equal them
F1= F2
M1g=GM1M2/R²
G=gR²/M2
g=GM2/R²

now part 2nd
we have mg=Gm1m2/r²
Density = mass / volume
mass=volume×density
volume of  sphere = 4/3
density =D
Mass=4/3r³×D
we have already proved that g=GM2/R²
put the value of M2 we drived
g=G4/3R³/R²
g=G4/3R
When the object is at a depth d below the surface of earth, it is attracted by the sphere of radius (R-d) only as the attraction due to the rest of earth cancel out. (At the centre of earth, the object would be attracted equally in all directions and the net force experienced by the object and hence the value of g would be zero)
Fdepth=Mg1=gm1m2/(R-d)²
M1=4/3(R-d)³
g1=4/3(R-d)³/(R-d)²
g1=4/3(R-d)

hence -------------g1=4/3π(R-d)
----------------------g=4/3πR
g1/g=4/3π(R-d)/4/3πR
g1=g{(R-d)R}.............................hence prove

2015-10-31T13:26:08+05:30
Please refer to the image.