The earth has a radius of 6380 km and turns around once on its axis in 24 h. (a) what is the radial acceleration of an object at the earth’s equator? give your answer in m/s2 and as a fraction of g. (b) if arad at the equator is greater than g, objects will fly off the earth’s surface and into space. what would the period of the earth’s rotation have to be for this to occur?

a) 0.03374 m/s²

b) 0.00343g

c) 5067 seconds or lower.

Explanation:

R = Radius of Earth = 6380000 m

T = Time period

= Radial acceleration

From Kepler's third law

g = Acceleration due to gravity = 9.81 m/s²

Radial acceleration is 0.03374 m/s²

1 g = 9.81 m/s²

Radial acceleration is 0.00343g

b) Here, we have considered

Hence, the time period of the earth’s rotation would be 5067 seconds.

Increasing the radial acceleration would decrease the time period further.

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