If the radius of the Earth were to increase while keeping its mass constant, wha

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Question: If the radius of the Earth were to increase while keeping its mass constant, what would happen to the value of g? (2023)

Options:

Correct Answer: g decreases

Exam Year: 2023

Solution:

If the radius increases while mass remains constant, g decreases because g = G * M / r^2.

If the radius of the Earth were to increase while keeping its mass constant, what would happen to the value of g? (2023)

If the radius of the Earth were to increase while keeping its mass constant, what would happen to the value of g? (2023)

Step 1: Understand that 'g' is the acceleration due to gravity at the surface of the Earth.
Step 2: Know that 'g' is calculated using the formula g = G * M / r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth.
Step 3: Recognize that if the radius (r) increases and the mass (M) stays the same, the value of r^2 (the radius squared) will also increase.
Step 4: Since g is inversely proportional to r^2, an increase in r^2 means that g will decrease.
Step 5: Conclude that if the radius of the Earth increases while keeping its mass constant, the value of g will decrease.

Gravitational Acceleration – The relationship between gravitational acceleration (g), mass (M), and radius (r) of a celestial body, described by the formula g = G * M / r^2.
Inverse Square Law – Understanding how changes in radius affect gravitational force due to the inverse square relationship.