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Question
Suppose unknowingly you wrote the universal gravitational constant value as G = 6.67 × 1011. instead of the correct value, G = 6.67 × 10−11, what is the acceleration due to gravity g' for this incorrect G? According to this new acceleration due to gravity, what will be your weight W'?
Solution
Data: Incorrect Gravitational constant G = 6.67 × 1011 Nm2 kg−2
Mass of the Earth Me = 5.972 × 1024 kg
Radius of the earth Re = 6371 km (or) 6371 × 103 m
Acceleration due to gravity g' = `"GM"_"e"/"R"_"e"^2`
g' = `(6.67 xx 10^11 xx 5.97 xx 10^24)/((6371 xx 10^3)^2)`
= `(39.8332 xx 10^35)/(4.0589641 xx 10^13)`
= 9.81 × 1022
g' = 1022 g
New weight W' = Mg' = M(1022 g) = 1022 mg
W' = 1022 W
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