If the mass of the Earth were to double, what would happen to the gravitational

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Question: If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?

Options:

Correct Answer: It would double

Solution:

If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.

If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?

If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?

Correct Answer: Gravitational force would double.

Step 1: Understand that gravitational force depends on mass and distance.
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 is the mass of the Earth, m2 is the mass of the object, and r is the distance from the center of the Earth to the object.
Step 3: Note that if the mass of the Earth (m1) doubles, we replace m1 with 2 * m1 in the formula.
Step 4: The new formula becomes F' = G * (2 * m1 * m2) / r^2.
Step 5: Compare the new force (F') with the original force (F). The new force is twice the original force: F' = 2 * F.
Step 6: Conclude that if the mass of the Earth doubles, the gravitational force on an object at its surface also doubles.

Gravitational Force – The gravitational force exerted by an object is directly proportional to its mass, as described by Newton's law of universal gravitation.
Newton's Law of Universal Gravitation – This law states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.