Question

Dirve and expretion for the vibration g with depth

Answer 1

Answer:-

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=  

3

4

​

πR  

3

×ρ

Substituting in equation ( 1 ) we get  

g=  

R  

2

 

G

​

×  

3

4

​

πR  

3

×ρ=  

3

4

​

πGRρ

g=  

3

4

​

πGRρ . . .. .. ( 2 )

g  

d

​

=  

3

4

​

πG(R−d)ρ  . . . .. .( 3 )

Dividing equation( 3 ) by ( 2 ) we get  

 

g

g  

d

​

 

​

=  

R

R−d

​

=(1−  

R

d

​

)

g  

d

​

=g(1−  

R

d

​

)

++++++++++++++++++++++++++++++++++++++++++++++++++++

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