The Earth’s radius is 6378.1 kilometers. If you were standing at the equator, yo

Question

The Earth’s radius is 6378.1 kilometers. If you were standing at the equator, you are essentially undergoing uniform circular motion with the radius of your circular motion being equal to the radius of the Earth. You are an evil mad scientist and have come up with the simultaneously awesome and terrifying plan to increase the speed of the Earth’s rotation until people at the Earth’s equator experience a centripetal (radial) acceleration with a magnitude equal to g, (9.81 m/s2 ), effectively making them experience weightlessness. If you succeed in your dastardly plan, what would be the new period of the Earth’s rotation?

a. 2.7 minutes b. 84 minutes c. 48 minutes d. 76 minutes

*answer given is b

Explanation / Answer

centripetal acceleration=v^2/r

r=6378.1 km =6378100 m

9.81=v^2/(6378100)

v=7910.06 m/s

period of roration=2*pi*r/v=5066.3 sec or 84 minutes

so answer is b

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