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Question
What would be the value of ‘g’ on the surface of the earth if its mass was twice and its radius half of what it is now?
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Solution
Given, Mass of the earth (M) = 2M
Radius of the earth (R') = `"R"/2`
Gravitational acceleration = g'
Formula: g = `("G""M")/("R"^2)`
Thus, g' = `("G" xx "M'")/("R'")^2 = ("G" xx 2"M")/("R"/2)^2`
⇒ g' = `("G" xx 2"M" xx 4)/"R"^2`
∴ g' = 8 g = 8 × 9.8
∴ g = 78.4 m/s2
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