If the Earth were to suddenly shrink in size but maintain its mass, what would h

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Question: If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?

Options:

Correct Answer: It would increase

Solution:

If the Earth shrinks in size while maintaining its mass, the gravitational force at the surface would increase due to the decrease in radius.

If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?

If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?

Step 1: Understand that gravity depends on mass and distance. The formula for gravitational force is 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 distance between the centers of the two masses.
Step 2: Recognize that if the Earth shrinks in size but keeps the same mass, the radius (r) of the Earth decreases.
Step 3: Note that in the formula, if the radius (r) gets smaller, the value of r^2 (the radius squared) also gets smaller.
Step 4: Since r^2 is in the denominator of the formula, a smaller r^2 means that the gravitational force (F) increases.
Step 5: Conclude that if the Earth shrinks in size while maintaining its mass, the gravitational force at its surface will increase.

Gravitational Force – The force of attraction between two masses, which depends on the mass of the objects and the distance between them.
Newton's Law of Universal Gravitation – The law that states that the gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers.
Radius and Gravitational Force Relationship – As the radius of a mass decreases while mass remains constant, the gravitational force at the surface increases due to the inverse square relationship.