If the radius of the Earth were to double, what would happen to the weight of an object on its surface?
Practice Questions
1 question
Q1
If the radius of the Earth were to double, what would happen to the weight of an object on its surface?
It would double
It would remain the same
It would become four times less
It would become four times more
Weight is proportional to 1/r^2; if the radius doubles, the weight becomes four times less.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of the Earth were to double, what would happen to the weight of an object on its surface?
Solution: Weight is proportional to 1/r^2; if the radius doubles, the weight becomes four times less.
Steps: 7
Step 1: Understand that weight is the force of gravity acting on an object.
Step 2: Know that the force of gravity depends on the mass of the Earth and the distance from the center of the Earth.
Step 3: The formula for weight (W) is W = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the object, and r is the radius of the Earth.
Step 4: If the radius of the Earth doubles, the new radius (r') is 2r.
Step 5: Substitute the new radius into the weight formula: W' = G * (m1 * m2) / (2r)^2.
Step 6: Simplify the equation: W' = G * (m1 * m2) / (4r^2).
Step 7: Notice that W' is 1/4 of the original weight (W), meaning the weight becomes four times less.
