Question

The formula for the force between two objects is F=GM/r^2, where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for G.

Answer 1

To isolate the gravitational constant G in the formula F = GMm/r², multiply both sides by r² and then divide by Mm to get G = Fr²/Mm.

Step-by-step explanation:

The formula given is the equation for Newton's universal law of gravitation, which can be rearranged to solve for the gravitational constant, G. To do this, we need to isolate G on one side of the equation. Starting with the formula F = GMm/r², we multiply both sides of the equation by r² to get Fr² = GMm, and then we divide both sides by Mm, resulting in G = Fr²/Mm.

This equation can be used to calculate the gravitational constant when the force F, the mass of Earth M, the mass of the object m, and the distance r are known. The gravitational constant G is a universal constant with the value of approximately 6.67 × 10⁻¹¹ Nm²/kg².

Answer 2

To solve for the gravitational constant G in the formula F = GM/r^2, we rearrange it to G = Fr^2/Mm. G is the gravitational constant with a value of approximately 6.67 × 10^{-11} Nm^2/kg^2, and is the same universally.

Step-by-step explanation:

The question involves solving the formula F = GM/r^2 for the gravitational constant G. This formula represents Newton's law of universal gravitation, where F is the force between two objects, M and m are their respective masses, G is the gravitational constant, and r is the distance separating the centers of mass of the two objects. To solve for G, you rearrange the formula as follows: G = Fr^2/Mm. This allows the calculation of the gravitational constant if the force F, masses M and m, and distance r are known. It's worth noting that the gravitational constant G has a value of approximately 6.67 × 10^{-11} Nm^2/kg^2 and is the same anywhere in the universe.