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Question

The value of acceleration due to gravity at height h from earth surface will become half its value on the surface if (R = radius of earth)

A
h=R
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B
h=2R
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C
h=(21)R
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D
h=(2+1)R
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Solution

The correct option is C. h=(21)R


The gravitational force acting on mass m on the surface of Earth is

F=GMmR2

mg=GMmR2
g=GMR2
gR2=GM.............(1)
where, g is acceleration due to gravity, G is gravitational constant, M is mass of Earth and R is radius of Earth.
Now, let the value of acceleration due to gravity at height h be g' then we have
g=GM(R+h)2
As per the problem,
g=g2=GM(R+h)2
g(R+h)2=2gR2................from (1)
(R+h)2=2R2
Taking roots from both sides, we get
R+h=2R
h=2RR
h=(21)R

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