What will be the gravitational force inside a hollow cylinder at the

[amaresh92]

what will be the gravitational force inside a hollow cylinder at the center?
if it is zero than explain why?
above thanks

 

[Petr Mugver]

If the cylinder has finite length, the field inside is zero only at the "center of the center", by symmetry considerations, and this even if the cylinder is not empty. If the cylinder has infinite length, then the field inside is zero not only along the axis, but in the whole region where there is no mass. The proof is the Gauss or divergence formula and the fact that for the gravitational field

$$\nabla\cdot E=4\pi G\rho$$.

 

[amaresh92]

what is meaning by center at center?

 

[Petr Mugver]

The center of the circular section at half longitudinal height

 

[PJC01]

The gravitational force inside a hollow cylinder at the center will be zero. This is because the gravitational force is directly proportional to the mass of an object and inversely proportional to the square of the distance between two objects. Since the center of a hollow cylinder is equidistant from all points on the inner surface of the cylinder, the distance between any two points at the center will be the same. Therefore, the gravitational force from all points on the inner surface will cancel each other out, resulting in a net force of zero. This is similar to the concept of gravity being zero at the center of a hollow sphere.