If the mass of the Earth were to double while its radius remains the same, what

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Question: If the mass of the Earth were to double while its radius remains the same, what would happen to the acceleration due to gravity? (2022)

Options:

Correct Answer: It would double

Exam Year: 2022

Solution:

If the mass of the Earth doubles, the acceleration due to gravity also doubles, as it is directly proportional to mass.

If the mass of the Earth were to double while its radius remains the same, what would happen to the acceleration due to gravity? (2022)

If the mass of the Earth were to double while its radius remains the same, what would happen to the acceleration due to gravity? (2022)

Step 1: Understand that gravity is affected by mass and distance. The formula for acceleration due to gravity (g) is g = G * (M / R^2), where G is the gravitational constant, M is mass, and R is radius.
Step 2: Identify that if the mass of the Earth (M) doubles, we replace M with 2M in the formula.
Step 3: Since the radius (R) remains the same, R^2 does not change.
Step 4: Substitute the new mass into the formula: g' = G * (2M / R^2).
Step 5: Notice that g' = 2 * (G * (M / R^2)), which means the new acceleration due to gravity (g') is double the original acceleration due to gravity (g).
Step 6: Conclude that if the mass of the Earth doubles, the acceleration due to gravity also doubles.

Gravitational Acceleration – The acceleration due to gravity is determined by the mass of the object and the distance from its center, following the formula g = G * (M/r^2), where g is the acceleration due to gravity, G is the gravitational constant, M is the mass, and r is the radius.