Given below are two statements: one is labelled as Assertion and the other is labelled as Reason .
Assertion : Earth has atmosphere whereas moon doesn’t have any atmosphere. Reason : The escape velocity on the moon is very small as compared to that on Earth.
Choose the correct answer from the options given below:
Both and are correct and is the correct explanation of
is false but is true
Both and are correct but is NOT the correct explanation of
is true but is false
Correct answer:A
Standard Method
Given: Assertion states that Earth has atmosphere whereas moon does not have any atmosphere.
Find: Whether Reason correctly explains Assertion .
Both Assertion and Reason are true.
The escape velocity is given by
Since the moon has smaller radius and smaller acceleration due to gravity compared to Earth, its escape velocity is much smaller.
Because of this lower escape velocity, gaseous particles can escape more easily from the moon, so it cannot retain an atmosphere like Earth.
Therefore, both and are correct, and is the correct explanation of . The correct option is A.
Conceptual Explanation
Given: Earth has an atmosphere, while the moon practically does not.
Find: Whether the lower escape velocity of the moon explains this difference.
The escape velocity is the minimum speed required for an object to escape the gravitational pull of a celestial body.
It is given by
where is the gravitational constant, is the mass of the planet, is its radius, and is the acceleration due to gravity.
The moon has smaller mass and smaller radius than Earth. Hence its escape velocity is much lower than that of Earth.
As a result, atmospheric gases can escape more easily from the moon. Earth, having a much larger escape velocity, is able to retain its atmosphere.
Thus Assertion is correct, Reason is correct, and Reason correctly explains Assertion . Hence the correct option is A.
Assuming that the moon has no atmosphere only because its mass is smaller. This is incomplete because the key retention condition is related to escape velocity. Always connect atmospheric retention to how easily gas molecules can escape.
Thinking that both statements are true but unrelated. This is incorrect because the lower escape velocity of the moon directly explains why it cannot retain atmospheric gases effectively.
Confusing escape velocity with acceleration due to gravity alone. Although matters, escape velocity depends on both gravitational effect and radius through .
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