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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=(√2−1)RThe gravitational force acting on mass m on the surface of Earth isF=GMmR2mg=GMmR2g=GMR2gR2=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 haveg′=GM(R+h)2As per the problem,g′=g2=GM(R+h)2g(R+h)2=2gR2................from (1)(R+h)2=2R2Taking roots from both sides, we getR+h=√2R∴h=√2R−R∴h=(√2−1)R

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