Numerical solution of the question...At what depth below the surface of earth,the value of 'g' is same as depth at a height 64 km above the surface of the earth. ???
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At height h above earth, g' = g*[R²/(R+h)²]
At depth d below the earth's surface, g' = g*[1 - d/R]
given that h = 64km
R = 6371km
d = ?
g*[R²/(R+h)²] = g*[1 - d/R]
⇒ R²/(R+h)² = 1 - d/R
⇒ 6371² / (6371+64)² = 1 - d/6371
⇒ 0.9802 = 1 - d/6371
⇒ d/6371 = 1-0.9802 = 0.0192
⇒ d = 6371*0.0192
⇒ d = 126 km
The depth is 126km.
At depth d below the earth's surface, g' = g*[1 - d/R]
given that h = 64km
R = 6371km
d = ?
g*[R²/(R+h)²] = g*[1 - d/R]
⇒ R²/(R+h)² = 1 - d/R
⇒ 6371² / (6371+64)² = 1 - d/6371
⇒ 0.9802 = 1 - d/6371
⇒ d/6371 = 1-0.9802 = 0.0192
⇒ d = 6371*0.0192
⇒ d = 126 km
The depth is 126km.
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