Attraction force of material curves and lines

Mass $M$ is uniformly distributed over the upper half ($y\geqslant 0$) of the circle $x^{2}+y^{2}=a^{2}$. With what force does it attract a point mass $m$ located at $(0,0)$?

A homogeneous rod of length $2 a$ has mass $M$. A material point of mass $m$ is located on the perpendicular bisector of from the rod at distance $b$ from its midpoint. With what force does the rod attract the point?

A homogeneous infinite rod has linear density $\rho$. A material point of mass $m$ is located at distance $l$ from the rod. With what force does the rod attract the point?

The leg $A B$ of a right triangle $A B C \; (\angle A = 90^{\circ })$ is a homogeneous material rod of length $4 a$ and mass $M$. At the vertex $C$ a material point of mass $m$ is placed, $A C = 3 a$:

A homogeneous infinite rod with linear density $\rho$ is bent into the shape of an angle. On the line containing the bisector of this angle there is a material point of mass $m$ at distance $h$ from the vertex of the angle. With what force does the rod attract the point?

In the Cartesian coordinate system $O x y$ a material line is given by the equation $y = 0$; its linear density varies according to the law $\rho (x) = \alpha \left|x\right|, \alpha > 0$. With what force does this line attract a point of mass $m$ located on the ordinate axis?

With what force does a homogeneous material half-ring of mass $M$ and radius $r$ attract a material point of mass $m$ located at its center?

A material circle has linear density $\rho$ and radius $r$. On the perpendicular to the plane of the circle passing through its center there is a material point of mass $m$ at distance $a$ from the center. With what force does the circle attract the point?

On the unit circle $x = \cos \varphi , y = \sin \varphi , 0 \leqslant \varphi \leqslant 2 \pi$, a charge is distributed with linear density

At the point $(a ; 0)$ there is a charge $q$. Find the force acting on this charge.

Prove, starting from the law of interaction of point masses, that a material curve $\Gamma$ with linear density $\rho (\xi ; \eta ; \zeta )$ attracts a mass $m$ located at the point $M(x ; y ; z)$ with force

Find the intensity of the gravitational field created by a homogeneous material line with linear density $\rho_{0}$.

With what force does a mass $M$, uniformly distributed along the circle $x^{2}+y^{2} = a^{2}, z = h > 0$, attract a point mass $m$ placed at the origin.