Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion (A): Earth has atmosphere and moon doesn’t Reason (R): escape speed on moon is less than that Earth. In the light of the above statements, choose the correct answer from the options given below
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion (A): Earth has atmosphere and moon doesn’t Reason (R): escape speed on moon is less than that Earth. In the light of the above statements, choose the correct answer from the options given below
(A) and (R) are correct and (R) is the correct explanation of (A)
(A) and (R) are correct and (R) is not the correct explanation of (A)
(A) is true but (R) is false
(A) and (R) both are false
The Correct Option is A
Approach Solution - 1
The correct answer is option (A): (A) and (R) are correct and (R) is the correct explanation of (A)
Both (A) and (R), are true and the escape speed on the moon is less due to its small radius and acceleration due to gravity as compared to earth.
Approach Solution -2
Escape Velocity and Atmospheres
Step 1: Understand the Concepts
The escape velocity (Vesc) is the minimum speed required for an object to escape the gravitational pull of a planet or celestial body. The formula for escape velocity is given by:
\( V_{esc} = \sqrt{\frac{2GM}{r}} = \sqrt{2gr} \)
Where:
- \( G \) is the gravitational constant.
- \( M \) is the mass of the planet.
- \( r \) is the radius of the planet.
- \( g \) is the acceleration due to gravity.
Step 2: Analyze the Assertion and Reason
Assertion A is correct: Earth has an atmosphere, while the moon does not.
Reason R states that the escape velocity on the moon is lower than on Earth.
Step 3: Determine the Relationship
The escape velocity depends on the mass and radius of the planet. The moon has a smaller mass and a smaller radius than Earth. This leads to a smaller escape velocity on the moon. This lower escape velocity is the reason why the moon has no atmosphere. Lighter particles, like the gases in an atmosphere, can reach escape velocity easier than heavier particles, and thus, the moon loses those lighter gases faster than Earth does.
Step 4: Determine the Correct Option
Both Assertion A and Reason R are correct, and Reason R is the correct explanation of Assertion A.
Conclusion:
The correct option is (1).
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].