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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?
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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