The Objects separated by gravitational force of 360 N, masses 6.25 × 10¹⁴ kg and 7.20 × 10⁵ kg. Applying Newton's law with G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² yields distance is 2.79139 km.
We can apply Newton's law of universal gravitation to calculate the distance between the two objects. The formula takes the form:
F = (G ⋅ m₁ ⋅ m₂) / r²
Where:
F represents the force between the two objects
G stands for the gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
m₁ and m₂ denote the masses of the two objects
r indicates the distance between the centers of the two objects
Given that the force F = 360 N, m₁ = 6.25 × 10¹⁴ kg, and m₂ = 7.20 × 10⁵ kg, we can solve for r:
r² = (G ⋅ m₁ ⋅ m₂) / F
r = √((G ⋅ m₁ ⋅ m₂) / F)
Now, substituting the values and solving for r:
r = √(((6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²) ⋅ (6.25 × 10¹⁴ kg) ⋅ (7.20 × 10⁵ kg)) / 360 N)
r ≈ 2791.39 m
Finally, converting the distance from meters to kilometers:
r ≈ 2.79139 km
Consequently, the two objects are approximately 2.79139 kilometers apart.
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When a wave transfers from one medium to another with different properties, the speed of the wave can change. In this case, we know that the wavelength changes when the wave transfers from the first type of rope to the second type of rope. If the wavelength becomes one-fourth of what it was before the transfer, this means that the second type of rope has a higher wave speed than the first type of rope.
The wave speed is defined as the product of the wavelength and the frequency of the wave. Since the frequency of the wave remains constant as it transfers from one medium to another, a decrease in wavelength means an increase in wave speed. This can be seen from the wave equation, c = λf, where c is the wave speed, λ is the wavelength, and f is the frequency.
Therefore, if the wavelength becomes one-fourth of what it was before the transfer, this means that the wave speed in the second type of rope is four times the wave speed in the first type of rope. In other words, the speed of the wave becomes quadruple its original speed after the transfer.
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A. There would be no difference in the results.
B. There would be half as many extraterrestrial civilizations.
C. There would be twice as many extraterrestrial civilizations.
D. There would be four times as many extraterrestrial civilizations.
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