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)
Practice Questions
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Q1
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)
It would double
It would remain the same
It would halve
It would increase by a factor of four
If the mass of the Earth doubles, the acceleration due to gravity also doubles, as it is directly proportional to mass.
Questions & Step-by-step Solutions
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Q
Q: 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)
Solution: If the mass of the Earth doubles, the acceleration due to gravity also doubles, as it is directly proportional to mass.
Steps: 6
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.
