Question

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

Solution
Verified by Toppr

( a ) The acceleration due to gravity on the earth is given by

g=GMR2i.e.GM=R2g . . . . . . .( 1 )

The acceleration due to gravity at height 'h' from the surface of the earth is given by

gh=GM(R+h)2i.e.GM=(R+h)2gh . . . . . . ( 2 )

From ( 1 ) and ( 2 ) we have,

ghg=R2(R+h)2

ghg=(12hR)

( 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 × density

M=43πR3×ρ

Substituting in equation ( 1 ) we get

g=GR2×43πR3×ρ=43πGRρ

g=43πGRρ . . .. .. ( 2 )

gd=43πG(Rd)ρ . . . .. .( 3 )

Dividing equation( 3 ) by ( 2 ) we get

gdg=RdR=(1dR)

gd=g(1dR)

Was this answer helpful?
41
Similar Questions
Q1

Which of the following graph correctly shows the variation of atmospheric pressure with altitude?


View Solution
Q2
Explain the variation of boiling point with altitude and why are we using a pressure cooker at high altitude for cooking?
View Solution
Q3

Discuss the pattern of variation in the oxidation states of
B to Tl

C to Pb

View Solution
Q4

Discuss the pattern of variation in the oxidation states of

(i) B to Tl and (ii) C to Pb.

View Solution
Q5

Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.

View Solution
Solve
Guides