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Question
Solve the following problem.
Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
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Solution
Given: M = 6 × 1024 kg, R = 6400 km = 6.4 × 106 m, g = 9.8 m/s2
To find: Gravitational constant (G)
Formula: g = `"GM"/"R"^2`
Calculation: From formula,
G = `"gR"^2/"M"`
G = `(9.8 xx (6.4 xx 10^6)^2)/(6 xx 10^24) = (401.4 xx 10^12)/(6 xx 10^24)`
∴ G = 6.69 × 10-11 Nm2/kg2
The value of gravitational constant is 6.69 × 10-11 Nm2/kg2 .
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