Question

At what height above the surface of the earth will the value of g be reduced by 36%

Answer 1

At what height will the acceleration due to gravity be reduced to 36% of its value on the surface of the Earth?

At the surface of the earth acceleration due to gravity is given by the relation

g=GM/R^2

Here

G =Universal gravitational constant

M =mass of the earth

R=radius of the earth

At the height h from the earth surface acceleration the to gravity g’ is

g’=GM/(R+h)^2

From above two relations we have

g’/g=[R/(R+h)]^2

Given

g’/g=36/100=[R/(R+h)]^2

Or. R/R+h=6/10

Or. 1+h/R=5/3

Or. h/R=2/3

h =2R/3=(2×6400/3)km

(since R=6400km)

=4266 km