Question

Discuss the variation of g with

(a) altitude (b) depth

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

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

$g=R_{2}GM i.e.GM=R_{2}g$ . . . . . . .( 1 )

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

$g_{h}=(R+h)_{2}GM i.e.GM=(R+h)_{2}g_{h}$ . . . . . . ( 2 )

From ( 1 ) and ( 2 ) we have,

$gg_{h} =(R+h)_{2}R_{2} $

$gg_{h} =(1−R2h )$

( b ) The acceleration due to gravity on the surface of the earth is given by.

$g=R_{2}GM $ . . . .( 1 )

let 'Q' be the density of the material of the earth.

Now, mass = volume $×$ density

$M=34 πR_{3}×ρ$

Substituting in equation ( 1 ) we get

$g=R_{2}G ×34 πR_{3}×ρ=34 πGRρ$

$g=34 πGRρ$ . . .. .. ( 2 )

$g_{d}=34 πG(R−d)ρ$ . . . .. .( 3 )

Dividing equation( 3 ) by ( 2 ) we get

$gg_{d} =RR−d =(1−Rd )$

$g_{d}=g(1−Rd )$

Solve any question of Gravitation with:-

Was this answer helpful?

0

0