Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the magnitude of the centripetal acceleration of a person standing on the equator? A) 0.00844 m/s² B) 0.00343 m/s² C) 0.0337 m/s² D) 0.343 m/s² E) 0.000854 m/s²

Question

Quizplus · Accepted Answer

The formula for centripetal acceleration is:
a = v^2/r
where v is the velocity and r is the radius of the circle (or in this case, the radius of the Earth).

The velocity of a person standing on the equator is equal to the velocity of the Earth's rotation, which is given by:
v = 2πr/T
where T is the period of rotation (one day).

Substituting in the values:
v = 2π(6.38 × 10^6 m)/(24 hours x 60 minutes x 60 seconds)
v = 463.8 m/s

Substituting this into the equation for centripetal acceleration:
a = (463.8 m/s)^2/(6.38 × 10^6 m)
a = 0.0337 m/s^2

Therefore, the answer is choice C.

Earth's Radius Is 6