The ratio between the values of accelaration due to gravity at a height 1km above and at a depth of 1km below the earth's surface is (radius of earth is R)

Answers (1)

Variation in 'g' with height -

g'=g\left ( \frac{R}{R+h} \right )^{2}

g'\rightarrow gravity at height h from surface of earth.

R\rightarrow Radius of earth

h\rightarrow height above surface
 

- wherein

g'\alpha\, \frac{1}{r^{2}}

r=R+h

 

  \text{Acceleration due to gravity above earth, } g_{1} = g_{o}\left ( 1-\frac{2h}{r} \right )
                                                                

 \text{Since h}< < \text{R acceleration due to gravity below earth surface. }g_{2}=g_{o}\left ( 1-\frac{d}{R} \right )

\because g_{1}=g_{2}

or g_{o}\left ( 1-\frac{2h}{R} \right )= g_{o}\left ( 1-\frac{d}{R} \right )

or d = 2h

d = 2 Km

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