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AakashPandita
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In my book it is written that Newton's shell theorem can be used to show that a uniform shell of matter exerts no net gravitational force on a particle located inside it. How?
How?Hardik Batra said:Like that the mass of all the spherical shell to be concentrate at the center of the shell.
AakashPandita said:how? if we take the centers of all the shells they would lie on the diameter.
I think this is the source of your confusion. You're thinking of dividing the sphere as if you were slicing a tomato - into very thin rings or discs of increasing(and after half-way through, decreasing) diametre, each ring having its centre lying along the radius of the sphere.Maybe I don't understand how the spherical shell is divided into infinite shells. Are they shaped like infinitesimally thin rings?
The concept of "proof of no net gravitational force on a particle inside uniform shell" refers to the idea that a particle placed inside a hollow spherical shell with uniform mass distribution will experience no net gravitational force from the shell. This is due to the principle of superposition, which states that the total force acting on a particle is the vector sum of all individual forces acting on it.
This concept is proven using the shell theorem, which states that the gravitational force on a particle inside a hollow spherical shell is only dependent on the mass inside the shell that is closer to the particle than the rest of the shell. This means that for a uniform shell, the mass on one side of the particle will be equal and opposite to the mass on the other side, resulting in a net gravitational force of zero.
Yes, this concept applies to all particles inside a uniform shell regardless of their position or mass. As long as the shell has a uniform mass distribution, the gravitational force on any particle inside will be zero.
This concept is significant because it helps us understand the effects of gravitational forces in a simple and predictable manner. It also helps to explain phenomena such as why objects on opposite sides of the Earth experience equal gravitational forces, even though they are at different distances from the center of the Earth.
This concept does not directly relate to the gravitational force outside of a uniform shell. However, it can be used to calculate the gravitational force on a particle outside of a uniform shell by treating the shell as a point mass located at its center. This allows for simplified calculations in cases where the shell has a large mass or is not uniformly distributed.