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?
It would double
It would remain the same
It would become half
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.
