If the mass of the Earth were to double while its radius remains the same, what
Practice Questions
Q1
If the mass of the Earth were to double while its radius remains the same, what would happen to the gravitational acceleration at its surface?
It would double
It would remain the same
It would halve
It would increase by a factor of four
Questions & Step-by-Step Solutions
If the mass of the Earth were to double while its radius remains the same, what would happen to the gravitational acceleration at its surface?
Correct Answer: g would double
Step 1: Understand that gravitational acceleration (g) depends on the mass of the object and the distance from its center.
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 radius (R) of the Earth remains the same.
Step 4: If the mass (M) of the Earth doubles, we can represent this as 2M.
Step 5: Substitute the new mass into the formula: g' = G * (2M / R^2).
Step 6: Compare the new gravitational acceleration (g') with the original gravitational acceleration (g = G * (M / R^2)).
Step 7: Since g' = 2 * (G * (M / R^2)), we see that g' = 2g.
Step 8: Conclude that if the mass of the Earth doubles, the gravitational acceleration at its surface also doubles.
Gravitational Acceleration – Gravitational acceleration at the surface of a planet is determined by the formula g = G * M / R^2, where G is the gravitational constant, M is the mass of the planet, and R is its radius.
Proportional Relationships – Understanding how changes in mass and radius affect gravitational acceleration, specifically that g is directly proportional to mass and inversely proportional to the square of the radius.
