Calculate the height above the surface of earth at which the value of acceleration due to gravity is half of what is on the surface
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The formula for these types of question is-
g'=g(1-2h/R)
So let's put the values of the variables
Since acceleration due to gravity at that height is half of g.
g'=g/2
g/2=g(1-2h/R)
1/2=(1-2h/R)
1=2(1-2h/R)
1=2-4h/R
-4h/R=1-2
-4h/R=-1
4h/R=1
h=R/4
h=6.4*10^6/4
h=1.6*10^6m
So your answer is 1600000 m or 1600km above the earth's surface.
g'=g(1-2h/R)
So let's put the values of the variables
Since acceleration due to gravity at that height is half of g.
g'=g/2
g/2=g(1-2h/R)
1/2=(1-2h/R)
1=2(1-2h/R)
1=2-4h/R
-4h/R=1-2
-4h/R=-1
4h/R=1
h=R/4
h=6.4*10^6/4
h=1.6*10^6m
So your answer is 1600000 m or 1600km above the earth's surface.
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