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The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

Grade:12

4 Answers

dev bhatnagar
8 Points
15 years ago

 

Acceleration due to gravity at a depth 'd' from earth surface is :


gd = g(1-   d  )
 R





Acceleration due to gravity at height 'h' from earth surface is :
h is very much smaller than R
gh = g(1-   2h  )
 R





gh = gd
By solving it , d=2h

Omkar ajit Darekar
33 Points
14 years ago
correct answer=gh = g(1- 2h ) R
Omkar ajit Darekar
33 Points
14 years ago

gh = g(1-   2h  )
 R
=correct answer

Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem below.
 
The acc. due to gravity at height h above earth, gh = g(1 – 2h/R)     [considering h
The acc. due to gravity at a depth d below the ground level, gd = g(1 – d/R)
Now equating, gd = gh
Hence, d = 2h
 
Hope it helps.
Thanks and regards,
Kushagra

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