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  • At what altitude above the earth surface would the accelaration due to gravity be half of it's value at the Earth's surface?( In kms)Option: 1 <

At what altitude above the earth surface would the accelaration due to gravity be half of it's value at the Earth's surface?( In kms)

Option: 1

2650


Option: 2

800


Option: 3

1600


Option: 4

2500


Answers (1)

best_answer

As we learnt

 

Variation in 'g' with height -

 

 

 

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

 

 

Here g'=g\left ( 1-\frac{2h}{R} \right ) will not be applicable because it is applicable for h<5% of radius of earth.

So,

\frac{g'}{g}= \frac{R^2}{\left ( R+h \right )^2}\Rightarrow \frac{g/2}{g}=\frac{R^2}{\left ( R+h \right )^2}\Rightarrow \frac{1}{2}=\frac{R^2}{\left ( R+h \right )^2}\Rightarrow \frac{1}{\sqrt{2}}= \frac{R}{\left ( R+h \right )}

R+h=\sqrt{2}R

h=\sqrt{2}R-R= R\left ( \sqrt{2} -1\right )= 6400\left ( 1.414-1 \right )= 2649.6km\approx 2650km

Posted by

vinayak

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