0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Derive an expression for acceleration due to gravity at a depth 'd' below the earth's earth surface.

Solution
Verified by Toppr

Let M be mass of the earth, R be the radius of the earth
gd be gravitational acceleration at depth d from the earth surface
g be gravitational acceleration on the earth surfaces.
p be the density of the earth.
p be the point inside the earth at depth d from earth surfaces.
CSCP=d, CP=Rd-----------(1) (since CS=R)
g=GMR2

g=G43πR3pR2

g=4GπRp3--------------(2)

gd= acceleration due to gravity at depth d

gd=G×MassofthespherewithradiusCPCp2

gd=G43πCP3ρCP2

gd=4GπCPρ3-----------(3)

Dividing eq. (3) by eq(2)

gdg=CPR=RdR

gd=g(1dR)

1197098_1231661_ans_5c63d8e9eb62490e97a9f98a37892c25.PNG

Was this answer helpful?
93
Similar Questions
Q1
Derive an expression for acceleration due to gravity at a depth 'd' below the earth's earth surface.
View Solution
Q2
Derive an expression for acceleration due to gravity at depth 'h' below earth's surface.
View Solution
Q3
The acceleration due to gravity at a height 2 km above the earth surface is same as that of acceleration due to gravity at depth d below the surface of earth. Then d is equal to
View Solution
Q4

The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface of earth for h << radius of earth


View Solution
Q5
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then:
View Solution