Earth (radius R) begins to spin faster about its axis until a person standing at latitude 60 degrees feels completely weightless. What will be the duration of one day under these conditions?

8*pi*sqrt(R/g)
8*pi*sqrt(g/R)
pi*sqrt(R/g)
4*pi*sqrt(g/R)

Correct answer: pi*sqrt(R/g)

Solution

Setting the centrifugal component equal to g at 60 deg latitude gives omega = 2*sqrt(g/R), and the period T = 2*pi/omega = pi*sqrt(R/g).

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