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If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would
  • a)
    decrease
  • b)
    remain unchanged
  • c)
    increase
  • d)
    be zero
Correct answer is option 'C'. Can you explain this answer?
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If the radius of the earth were to shrink by one percent, its mass rem...

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If the radius of the earth were to shrink by one percent, its mass rem...
Would increase.

The acceleration due to gravity on Earth, denoted as "g," is inversely proportional to the square of the radius of the Earth. Mathematically, it can be expressed as:

g ∝ 1/r²

Where "r" is the radius of the Earth. If the radius of the Earth were to shrink by one percent, the new radius would be (1 - 0.01)r = 0.99r.

Substituting the new radius into the equation, we have:

g' ∝ 1/(0.99r)²
= 1/(0.9801r²)
≈ 1.0204/r²

Comparing this to the original equation, we can see that the new acceleration due to gravity, g', is greater than the original acceleration due to gravity, g. Therefore, if the radius of the Earth were to shrink by one percent while keeping the mass constant, the acceleration due to gravity on the Earth would increase.
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If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface woulda)decreaseb)remain unchangedc)increased)be zeroCorrect answer is option 'C'. Can you explain this answer?
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