Question:
What is the reason for earth not moving towards the moon, even though moon attracts the earth ?
What is the reason for earth not moving towards the moon, even though moon attracts the earth ?
Updated On: May 15, 2024
- The mass of the earth is much larger than the mass of the moon, it accelerates at a rate lesser than the acceleration rate of the moon towards the earth
- The mass of the moon is much larger than the mass of the earth, it accelerates at a rate lesser than the acceleration rate of the earth towards the moon
- The mass of the earth is similar to that of the moon, and both accelerate at a same rate
- Both experience unequal gravitational forces from each other
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The Correct Option is A
Solution and Explanation
Earth and the moon experience equal magnitude o f gravitational force due to each other
Acceleration of moon, $a_{m}=\frac{F}{M_{m}}$
Acceleration of earth, $a_{e} =\frac{F}{M_{e}}$
Since $M_{e} > > \, M_{m}$ so $a_{e} << a_{m}$
Acceleration of moon, $a_{m}=\frac{F}{M_{m}}$
Acceleration of earth, $a_{e} =\frac{F}{M_{e}}$
Since $M_{e} > > \, M_{m}$ so $a_{e} << a_{m}$
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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].