ИДЗ 13.3 – Вариант 14. Решения Рябушко А.П.

1. Calculate the mass of the D heterogeneous plate, given the limited lines, if the areal density at each point μ = μ (x, y)

1.14. D: x = 0, y = 0, x + y = 1, μ = 2x2 + y2

2. Calculate the static moment of a homogeneous plate the D, limited data lines, with respect to said axis, using polar coordinates.

2.14. D: x2 + y2 - 2ax = 0, x2 + y2 - ax = 0, y ≥ 0, Oy

3. Calculate the coordinates of the center of mass of a homogeneous body, occupying the area of the V, bounded by said surfaces.

3.14. V: 4y = √x2 + z2, x2 + z2 = 16, y = 0

4. Calculate the moment of inertia with respect to said homogeneous body axes, occupying the area of the V, the limited data surfaces. body density δ taken equal to 1.

4.14. V: z = x2 + y2, z = 3, Oz

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