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  • 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)Op

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)

Option: 1

\frac{R-2}{R-1}


Option: 2

 \frac{R}{R-1}


Option: 3

 \frac{R-2}{R}


Option: 4

 \frac{2R}{R-1}


Answers (1)

best_answer

As we learnt  

 

Variation in 'g' with depth -

 

g'=g\left [ 1-\frac{d}{R} \right ]

d\rightarrow depth from the surface of earth

g'\rightarrow Value of g at depth 'd'
 

- wherein

'g' decreases on going below the surface of earth .

g'\alpha (R-d)

 

 If h<<<<R then gravity at height 

g_h=g\left ( 1-\frac{2h}{R} \right )..........(1)

And gravity at depth d 

g_d=g\left ( 1-\frac{d}{R} \right )..........(2)

\frac{g_h}{g_d}=\frac{\left ( 1-\frac{2h}{R} \right )}{\left ( 1-\frac{d}{R} \right )}=\left ( \frac{R-2h}{R-d} \right )

At h=d=1km

\frac{g_h}{g_d}=\left ( \frac{R-2}{R-1} \right )

 

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