A uniform, spherical, 1000.0-kg shell has a radius of 5.00 m. (b)...

Question

A uniform, spherical, 1000.0-kg shell has a radius of 5.00 m. (b) Sketch a qualitative graph of the magnitude of the gravitational force this sphere exerts on a point mass m as a function of the distance r of m from the center of the sphere. Include the region from r = 0 to r -> ∞.

Accepted Answer

Hey, everyone. Welcome back in this problem, we have a thin rogue planet in the form of a homogeneous spherical shell of mass, big M and radius big R floats through space without orbiting any star were asked to draw a graph that illustrates the variation of the gravitational force on a point like object of math little out moving away radia lee from the center of the planet to a point at infinity. The answer choices here are graphs, we have four different answer choices of this graph. So let's walk through what the graph should look like. So let's think about an object that lies outside of this planet. Okay. So outside of this planet, what's going to happen? Well, outside of the planet, okay. Recall that the force of gravity F G, the gravitational force is going to be inversely proportional to the distance from the center, which in this case is going to be a little R. So if we're outside of the planet, the force of gravity is going to be inversely proportional to the distance from the center which is little are now outside of the planet means that the little R, the radius that we're at is going to be greater than big R, the radius of the planet. Alright. So for little R, which is represented in our X axis greater than the value of bigger, we have F G inversely proportional to the distance. Now, if we look at our answer choices, A B C and D, we actually see this relationship represented in all three of those. Okay. For little are bigger than big R. Okay. So in our graph, when we're talking about being to the right of big R on our X axis, all of these graphs show this inverse relationship. Alright. So we are able to eliminate any what about inside the plan, what happens inside the planet? So this is gonna be when little R is less than bigger. Well, we have a spherical shell okay. A homogeneous spherical shell. So it's not like the earth, it's a little bit simpler. So because we have a homogeneous spherical shell, we're called that the gravitational force F G let's call it Is going to be equal to zero. So because we have a homogeneous spherical shell and we don't have mass inside of our planet and we are inside that outer radius, that outer shell, hey, where little R is less than bigger than our gravitational forces just here. So if we look back at our answer choices, we see that that corresponds with answer choice C K. The first part of the graph from an X value of zero to an X value of big are, the function lies at zero. And then once the function hits a radius of big, are we switch to this inverse relationship between the gravitational force and the radius or distance from the center are? And so we have answer choice C here and that's it for this one. Thanks everyone for watching. See you in the next video.

A uniform, spherical, 1000.0-kg shell has a radius of 5.00 m. (b) Sketch a qualitative graph of the magnitude of the gravitational force this sphere exerts on a point mass m as a function of the distance r of m from the center of the sphere. Include the region from r = 0 to r -> ∞.

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