JEE Mains · Physics · STD 11 - 7. gravitation

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) Earth has atmosphere whereas moon doesn't have any atmosphere. Reason \(R\) : The escape velocity on moon is very small as compared to that on earth. In the light of the above statement, choose the correct answer from the options given below :

A \(A\) is true but \(R\) is false
B \(A\) is false but \(R\) is true
C Both \(A\) and \(R\) are correct but \(R\) is \(NOT\) the correct explanation of \(A\)
D Both \(A\) and \(R\) are correct and \(R\) is correct explanation of \(A\)

Verified Solution

Answer & Solution

Correct Answer

(D) Both \(A\) and \(R\) are correct and \(R\) is correct explanation of \(A\)

Step-by-step Solution

Detailed explanation

At Moon, due to low escape velocity, the rms velocity of molecules is greater than escape velocity. Hence molecules escape and there is no atmosphere at Moon.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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