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An object is located at a distance R/2 from the centre of the Earth (inside it). Assuming the Earth has uniform density, what is the gravitational acceleration at that point? (g is surface gravity, R is Earth's radius.)

1. g
2. 2 g
3. g/2
4. none of these

Correct answer: g/2

Solution

For a uniform-density sphere, only the mass within radius r contributes, giving g(r) = g*(r/R). At r = R/2, g(R/2) = g*(1/2) = g/2.

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