Two spheres (m_(1) and m_(2)) are separated a distance d, apart. The gravitational force between the two spheres is 41 N. If the spheres are separated to a distance of 3 times the original distance what is the new gravitational force between the spheres? m1 m2

The gravitational force between two masses is given by Newton's law of universal gravitation: where:- is the gravitational force,- is the gravitational constant (\(6.674 \times 10^{-11} \, \text{N}\cdot(\text{m/kg})^2\)),- and are the masses of the two spheres,- is the distance between the centers of the two masses.Initially, the gravitational force is 41 N when the distance is . If the distance is increased to 3 times the original distance, the new distance becomes .The new gravitational force can be calculated using the same formula, but with the new distance: This simplifies to: Since the initial force , we can express in terms of : Substituting the known value of : Therefore, the new gravitational force between the spheres when they are separated by a distance of 3 times the original distance is approximately 4.56 N.