If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?
Practice Questions
1 question
Q1
If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?
It would increase
It would decrease
It would remain the same
It would become zero
If the Earth shrinks in size while maintaining its mass, the gravitational force at the surface would increase due to the decrease in radius.
Questions & Step-by-step Solutions
1 item
Q
Q: If the Earth were to suddenly shrink in size but maintain its mass, what would happen to the gravitational force at its surface?
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.
Steps: 5
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.
