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 1

Answer:

b. 84 minutes

Explanation:

$a_c=g$ = Centripetal acceleration = 9.81 m/s²

r = Radius of Earth = 6378.1 km

v = Velocity

Centripetal acceleration is given by

$a_c=\dfrac{v^2}{r}\\\Rightarrow v=\sqrt{a_cr}\\\Rightarrow v=\sqrt{9.81\times 6378100}\\\Rightarrow v=7910.06706\ m/s$

Time period is given by

$T=\dfrac{2\pi r}{v60}\\\Rightarrow T=\dfrac{2\pi 6378.1\times 10^3}{7910.06706\times 60}\\\Rightarrow T=84.43835\ minutes$

The time period of Earth’s rotation would be 84.43835 minutes

Answer 2

The new period of the Earth’s rotation is mathematically given as

T=84.43835 min

What would be the new period of the Earth’s rotation?

Question Parameter(s):

The Earth’s radius is 6378.1 kilometers.

g= (9.81 m/s2 ),

Generally, the equation for the   is mathematically given as
$a_c=\dfrac{v^2}{r}$

Therefore

$v=\sqrt{a_cr}\\\\v=\sqrt{9.81*6378100}$

v=7910.06706 m/s

In conclusion

$T=\dfrac{2\pi r}{v60}$

Hence

$T=\dfrac{2\pi 6378.1*10^3}{7910.06706*60}$

T=84.43835 min

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