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If the Earth shrinks in its size (radius) mass remaining the same, the value of g on its surface will
If the Earth shrinks in its size (radius) mass remaining the same, the value of g on its surface will
Updated On: Jun 8, 2024
- increase
- decrease
- remain same
- be reduced to zero
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The Correct Option is A
Solution and Explanation
Acceleration due to gravity of the Earth is given by
$g = \frac{GM}{R^2}$ or $g \propto \frac{1}{R^2}$ (for same mass)
If the Earth shrinks in its size, mass remaining same, the value of g on its surface will increase.
$g = \frac{GM}{R^2}$ or $g \propto \frac{1}{R^2}$ (for same mass)
If the Earth shrinks in its size, mass remaining same, the value of g on its surface will increase.
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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].
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