Two uniform spheres, each with mass M and radius R, touch each ot...

Question

Two uniform spheres, each with mass M and radius R, touch each other. What is the magnitude of their gravitational force of attraction?

Accepted Answer

Welcome back everybody. We are looking at two spherical masses used for shot put and we are told a couple of different things here, we are told that for each uh spherical mass it's gonna have some mass M. And then some diameter D. Right now we are told the distance between them is half of the diameter A. K. A. The radius. And we are asked to find what the gravitational force is between these two objects. Well, according to kepler's laws, right, the gravitational force between two objects is going to be New Newton's gravitational constant times the mass of the first object times the mass of the second object all over the distance between their centers. Well, the centers are right here. Right? And so this distances are and this distances are meaning this entire distance between their centers is three R. And we also know that both objects have the same mass. So let's actually simplify this a little bit. The gravitational force between them is really going to be equivalent to Newton's gravitational constant times the mass is squared all over three R squared. But if you look at all our answers here, we need our answer in terms of diameter. So I'm actually gonna put whole this three R squared terms aside. And I'm gonna simplify this, right? So this is really equivalent to three times the diameter divided by two squared. Which gives us nine D squared over four. Plugging this back into our equation. We have uh Newton's gravitational constant times our mass is squared divided by this fraction. Which when you divide by a fraction you just multiplied by its reciprocal. So this could be four time, or it's four divided by nine D squared, giving us that our gravitational force is four times big. G. Times the mass is squared, all divided by nine D. Squared, corresponding to our final answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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