4 is the answer to this question
We have that The ratio U1/U2 of their potential energies due to their interactions with Q is
From the question we are told that
Question 1
Charge q1 is distance r from a positive point charge Q.
Question 2
Charge q2=q1/3 is distance 2r from Q.
Charge q1 is distance s from the negative plate of a parallel-plate capacitor.
Charge q2=q1/3 is distance 2s from the negative plate.
Generally the equation for the potential energy is mathematically given as
Therefore
The Equations of U1 and U2 is
For U1
For U2
Since
U is a function of q and q2=q1/3
Therefore
For Question 2
For U1
Therefore
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Based on all we know about the terrestrial worlds, the single factor appears to play the most important role in a terrestrial planet's geological destiny is size size of terrestrial planet .
According to the question
Terrestrial Planets:
They belongs to a class of planets that are like the earth
Geological destiny :
Geology is biological destiny: Whatever minerals land or are deposited in a place determine what or who can make a living there millions of years later
Based on all we know about the terrestrial worlds, what single factor appears to play the most important role in a terrestrial planet's geological destiny
i.e
The size of terrestrial planet is one of the factors to play the most important role in a terrestrial planet's geological destiny
which determines how long the planet can retain internal heat, which drives geological activity because Smaller worlds cool off faster and harden earlier .
Hence, Based on all we know about the terrestrial worlds, the single factor appears to play the most important role in a terrestrial planet's geological destiny is size size of terrestrial planet .
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