Question

# Discuss the variation of g with(a) altitude (b) depth

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#### ( a ) The acceleration due to gravity on the earth is given byg=GMR2i.e.GM=R2g . . . . . . .( 1 )The acceleration due to gravity at height 'h' from the surface of the earth is given bygh=GM(R+h)2i.e.GM=(R+h)2gh . . . . . . ( 2 )From ( 1 ) and ( 2 ) we have,ghg=R2(R+h)2ghg=(1−2hR) ( b ) The acceleration due to gravity on the surface of the earth is given by.g=GMR2 . . . .( 1 )let 'Q' be the density of the material of the earth.Now, mass = volume × densityM=43πR3×ρSubstituting in equation ( 1 ) we get g=GR2×43πR3×ρ=43πGRρg=43πGRρ . . .. .. ( 2 )gd=43πG(R−d)ρ . . . .. .( 3 )Dividing equation( 3 ) by ( 2 ) we get gdg=R−dR=(1−dR)gd=g(1−dR)

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