If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?
Practice Questions
1 question
Q1
If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?
It would double
It would remain the same
It would increase by a factor of four
It would decrease by half
If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.
Questions & Step-by-step Solutions
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Q
Q: If the mass of the Earth were to double, what would happen to the gravitational force it exerts on an object at its surface?
Solution: If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.
Steps: 6
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.
