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 of Earth.
In the light of the above statements, choose the correct answer from the options given below:
Assertion (A): Earth has atmosphere and moon doesn’t
Reason (R): escape speed on moon is less than that of 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
Solution and Explanation
The correct option is (A): (A) and (R) are correct and (R) is the correct explanation of (A)
\(V_{esc}=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G}{R}\times \frac{\rho 4}{3}\pi R^{3}}\)
\(V_{esc}\propto R\)
As the moon's radius is very small as compared to earth. \(V_{esc}\) at the moon is quite low and the gas molecules attains escape velocity at normal temperature on the moon.
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Concepts Used:
Gravitation
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- 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].