Attraction force of plane and surface masses

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A material disk of radius rr has surface density ρ\rho. On the perpendicular to the plane of the disk passing through its center there is a material point of mass mm at distance aa from the center. With what force does the disk attract the point?

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A material plane has surface density ρ\rho. With what force does the plane attract a material point of mass mm located at distance aa from the plane?

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Find the magnitude of the force with which a homogeneous surface:

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(1)

x=acos⁡φ,y=asin⁡φ,z=z,φ∈[0;2π],z∈[0;H]x = a \cos \varphi , y = a \sin \varphi , z = z, \varphi \in [0 ; 2 \pi ], z \in [0 ; H];

(2)

x=rcos⁡φ,y=rsin⁡φ,z=r,φ∈[0;2π],r∈[a;b],a>0x = r \cos \varphi , y = r \sin \varphi , z = r, \varphi \in [0 ; 2 \pi ], r \in [a ; b], a > 0; of density ρ0\rho_{0}, attracts a point mass mm placed at the origin.

Find the force of attraction of a material point of mass mm with coordinates (0;0;h)(0 ; 0 ; h) by a material disk {x2+y2⩽R2,z=0}\left\{ x^{2}+y^{2} \leqslant R^{2}, z = 0\right\}, over which mass is uniformly distributed with surface density ρ0\rho_{0}.

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Find the force of attraction of a material point of mass mm with coordinates (0;0;h)(0 ; 0 ; h) by a material plane, over which mass is uniformly distributed with surface density ρ0\rho_{0}.

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References

[ККЧ+03a] Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. Интегралы. Ряды. 2-е изд., ФИЗМАТЛИТ, 2003.
[ККЧ+03b] Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. Функции многих переменных. 2-е изд., ФИЗМАТЛИТ, 2003.