A space station is designed to simulate gravity through rotation. If the station has a radius of 100 m and needs to simulate Earth's gravity (9.8 m/s²), what should be its rotational period?

Core Concept

The centripetal acceleration at the edge of the station is a = v²/r = 4π²r/T². Setting this equal to g: g = 4π²r/T², so T = 2π√(r/g) = 2π√(100/9.8) ≈ 20 s. Option A is incorrect as it's half the required period. Option C is incorrect as it's 1.5 times the required period. Option D is incorrect as it's double the required period.