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If the Earth were to suddenly shrink to half its radius while maintaining its ma

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Question: If the Earth were to suddenly shrink to half its radius while maintaining its mass, what would happen to the gravitational force at its surface?

Options:

  1. It would double
  2. It would remain the same
  3. It would become half
  4. It would become four times stronger

Correct Answer: It would become four times stronger

Solution: 

The gravitational force at the surface is inversely proportional to the square of the radius. If the radius is halved, the force becomes four times stronger.

If the Earth were to suddenly shrink to half its radius while maintaining its ma

Practice Questions

Q1
If the Earth were to suddenly shrink to half its radius while maintaining its mass, what would happen to the gravitational force at its surface?
  1. It would double
  2. It would remain the same
  3. It would become half
  4. It would become four times stronger

Questions & Step-by-Step Solutions

If the Earth were to suddenly shrink to half its radius while maintaining its mass, what would happen to the gravitational force at its surface?
  • Step 1: Understand that gravitational force depends on mass and distance from the center of the object.
  • Step 2: Recall the formula for gravitational force: F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance (radius).
  • Step 3: Note that if the Earth shrinks to half its radius, the new radius (r) becomes r/2.
  • Step 4: Substitute the new radius into the formula: F' = G * (m1 * m2) / (r/2)^2.
  • Step 5: Simplify the equation: (r/2)^2 = r^2 / 4, so F' = G * (m1 * m2) / (r^2 / 4) = 4 * (G * (m1 * m2) / r^2).
  • Step 6: This shows that the new gravitational force (F') is four times the original force (F).
  • Step 7: Conclude that if the Earth shrinks to half its radius, the gravitational force at its surface becomes four times stronger.
  • Gravitational Force – The gravitational force at the surface of a planet is determined by the formula F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the radius.
  • Inverse Square Law – The gravitational force is inversely proportional to the square of the distance (or radius) from the center of the mass.
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