If the radius of the Earth were to increase by a factor of 2, what would happen
Practice Questions
Q1
If the radius of the Earth were to increase by a factor of 2, what would happen to the gravitational acceleration at its surface?
It would double
It would remain the same
It would halve
It would become one-fourth
Questions & Step-by-Step Solutions
If the radius of the Earth were to increase by a factor of 2, what would happen to the gravitational acceleration at its surface?
Step 1: Understand that gravitational acceleration (g) depends on the mass of the Earth and the distance from its center (radius).
Step 2: Know that if the radius of the Earth increases, the distance from the center to the surface increases.
Step 3: Remember the formula for gravitational acceleration: g = G * M / r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the radius.
Step 4: If the radius (r) doubles, we replace r with 2r in the formula: g = G * M / (2r)^2.
Step 5: Calculate (2r)^2, which equals 4r^2.
Step 6: Substitute this back into the formula: g = G * M / 4r^2.
Step 7: Notice that this means g is now 1/4 of what it was before because we have divided by 4.
Step 8: Conclude that if the radius of the Earth doubles, the gravitational acceleration at its surface becomes 1/4 of the original value.
Gravitational Acceleration – Gravitational acceleration at the surface of a planet is determined by the mass of the planet and the distance from its center, following the formula g = G * M / r^2.
Inverse Square Law – The gravitational force and acceleration are inversely proportional to the square of the distance from the center of the mass.
