Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m high ladders. The centre of mass of the Earth (mE = 5.90 $\times$ 1024 kg) is then displaced:
A)0 m.
B)1.84 *10-23 m.
C)1.84 * 10-14 m.
D)1.80 * 10-13 m.
E)2 m.

Question

Quizplus · Accepted Answer

The displacement of the center of mass of the Earth can be calculated using the formula:
Δx = (m * g * h) / F
where m is the total mass of the people, g is the acceleration due to gravity, h is the height they climbed, and F is the gravitational force between the people and the Earth.

The total mass of the people is:
m = 1 billion * 55 kg = 5.5 * 10^10 kg

The gravitational force between the people and the Earth is:
F = G * mE * m / R^2
where G is the gravitational constant and R is the radius of the Earth.

Assuming that all the people are standing on the same point on the Earth's surface, the radius R remains constant, and we can simplify the equation to:
F = G * mE * m / R^2 = (6.67 * 10^-11 N*m^2/kg^2) * (5.9 * 10^24 kg) * (5.5 * 10^10 kg) / (6.37 * 10^6 m)^2 = 5.46 * 10^18 N

Substituting the values into the formula, we get:
Δx = (5.5 * 10^10 kg * 9.81 m/s^2 * 2 m) / (5.46 * 10^18 N) = 1.84 * 10^-14 m

Therefore, the center of mass of the Earth is displaced by 1.84 * 10^-14 m. Choice C is the best option.

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