If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at the surface? (2023)
Practice Questions
1 question
Q1
If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at the surface? (2023)
It increases
It decreases
It remains the same
It becomes zero
Gravitational acceleration is inversely proportional to the square of the radius. If radius increases, g decreases.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at the surface? (2023)
Solution: Gravitational acceleration is inversely proportional to the square of the radius. If radius increases, g decreases.
Steps: 6
Step 1: Understand that gravitational acceleration (g) is affected by the mass of an object and the distance from its center (radius).
Step 2: Recall the formula for gravitational acceleration: g = G * (M / R^2), where G is the gravitational constant, M is the mass, and R is the radius.
Step 3: Note that in this scenario, the mass (M) of the Earth remains constant.
Step 4: Recognize that if the radius (R) of the Earth increases, the value of R^2 (the radius squared) also increases.
Step 5: Since g is inversely proportional to R^2, an increase in R^2 means that g will decrease.
Step 6: Conclude that if the radius of the Earth increases while keeping its mass constant, the gravitational acceleration at the surface will decrease.
