If the mass of the Earth were to double, what would happen to the gravitational
Practice Questions
Q1
If the mass of the Earth were to double, what would happen to the gravitational force between the Earth and an object on its surface?
It would double
It would remain the same
It would halve
It would quadruple
Questions & Step-by-Step Solutions
If the mass of the Earth were to double, what would happen to the gravitational force between the Earth and an object on its surface?
Step 1: Understand that gravitational force (F) depends on the mass of the Earth (M) and the mass of the object (m) according to the formula F = G * (M * m) / r^2, where G is the gravitational constant and r is the distance between the centers of the two masses.
Step 2: Recognize that if the mass of the Earth (M) doubles, we can represent this as 2M.
Step 3: Substitute 2M into the gravitational force formula: F' = G * (2M * m) / r^2.
Step 4: Notice that F' = 2 * (G * (M * m) / r^2), which means the new gravitational force (F') is twice the original gravitational force (F).
Step 5: Conclude that if the mass of the Earth doubles, the gravitational force between the Earth and an object on its surface also doubles.
Gravitational Force – The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers, as described by Newton's law of universal gravitation.
Proportional Relationships – Understanding how changes in mass affect gravitational force, specifically that if one mass increases, the gravitational force increases proportionally.
