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How far away from the surface …

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How far away from the surface of earth does the value of g is reduced to 4% of its value on the surface of the earth given radius of earth 6400 km
  • 1 answers

Sia ? 6 years ago

We know that acceleration due to gravity from the surface of Earth at height "h" is given as,

{tex}g' = g \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
 reduced to 4% of gravity due to earth g' = 4% of {tex}g' = \frac { 4 g } { 100 }{/tex}
R = 6400km
{tex}\frac { 4 g } { 100 }= g \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
{tex}\frac { 4 } { 100 } = \left( \frac { R } { R + h } \right) ^ { 2 }{/tex}
{tex}\frac { 2 } { 10 } = \frac { R } { R + h }{/tex}
2(R + h) = 10R

2R+2h=10R
2h =10R-2R

2h=8R

h=8R/2
h = 4R

h= 4 {tex}\times{/tex} 6400

h= 25,600km.

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