If the radius of earth shrinks by $2 \%$ while its mass remains same The acceleration due to gravity on the earth's surface will approximately :
- decrease by $2 \%$
decrease by $4 \%$
increase by \(2%\)%
- increase by $4 \%$
The Correct Option is D
Solution and Explanation
From the given options the correct answer is option (D): increase by 4%
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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].