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  • Answer please! 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 :

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 :

  • Option 1)

    \text{d} = \frac{1} {2}\text{km}

  • Option 2)

    \text{d} = 1\,\text{km}

  • Option 3)

    \text{d} = \frac{3} {2}\text{km}

  • Option 4)

    \text{d} = 2\,\text{km}

 

Answers (1)

best_answer

 

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

 

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

Since h<<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


Option 1)

\text{d} = \frac{1} {2}\text{km}

This option is incorrect.

Option 2)

\text{d} = 1\,\text{km}

This option is incorrect.

Option 3)

\text{d} = \frac{3} {2}\text{km}

This option is incorrect.

Option 4)

\text{d} = 2\,\text{km}

This option is correct.

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perimeter

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