Question

Two objects exert a gravitational force on 8 N on one another. What would that force be if the mass of BOTH objects were doubled?

Answer 1

Based on Newton's law of universal gravitation, the equation for the gravitational force exerted by an object on another object is given by:
F = Gm1m2/(r^2)
where G is the universal gravitational constant, F is the gravitational force exerted, m1 is the mass of the first object, m2 is the mass of the second object, and r is the separation distance between the two objects.
If the mass of both objects were doubled, then we would have: m1' * m2' = (2m1) * (2m2) = 4m1m2. Assuming r stays constant (G is a constant so that won't change anyway), then this means that the new force will be 4 times greater, ie 8N * 4 = 32N of gravitational force.