Answer:
The new force of gravity between A and the doubled mass B, when the distance is quadrupled, can be found using the inverse square law of gravity, which states that the force is inversely proportional to the square of the distance and directly proportional to the product of the masses.
To find the new force, we can use the following equation:
F_new = (G * m_A * m_B') / d_new^2
where G is the gravitational constant, m_A is the mass of object A, m_B' is the new mass of object B (doubled), and d_new is the new distance between objects A and B (quadrupled).
Substituting the values, we get
F_new = (G * m_A * 2m_B) / (4d)^2
Simplifying, we get:
F_new = F_original / 16
Therefore, the new force is one-sixteenth (1/16) of the original force, or:
F_new = 100 N / 16 = 6.25 N.
So the new force between objects A and B is 6.25 N.