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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The earth has an atmosphere whereas the moon does not have any atmosphere.
Reason R: The escape velocity on the moon is very small as compared to that on the earth.

Asked in JEE Main 6th April 2nd Shift 2023 · Escape velocity formula

Answer: (2) Both A and R are correct and R is the correct explanation of A.

Step-by-step solution

A planet keeps a gas only if the typical speed of its molecules stays well below the escape speed at its surface.

The moon's escape speed is about 2.4 km/s against the earth's 11.2 km/s, because vₑ=√(2GM)/R and the moon is both lighter and smaller.

At lunar temperatures a fair share of the molecules in the tail of the speed distribution exceed 2.4 km/s, so any gas leaks away over time.

Both statements are correct and the small escape speed is exactly why the moon has no atmosphere.

Why the other options are wrong

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