d) A solid homogeneous sphere of radius R and density p is deformed by its own gravitational field with the force per un

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D A Solid Homogeneous Sphere Of Radius R And Density P Is Deformed By Its Own Gravitational Field With The Force Per Un 1 (57.38 KiB) Viewed 29 times

d) A solid homogeneous sphere of radius R and density p is deformed by its own gravitational field with the force per unit mass given by -gr/R, where g is the gravitational acceleration and r is the radius-vector from the centre of the sphere. Find the pressure in the centre of the sphere. [8] Hint: The relevant components of the deformation tensor in spherical coordinates are given by dur Up Up Upr = " Ꮂ Ꮎ Ꮎ Upp Ər r The relevant differential operators are given by Ə 18 𐐀ur ▼ er Ə Ər' (V²u), = 1200 (r² ur)), V. u= +2ur Ər r² Ər Ər r e) Find what portion of the volume of the sphere is compressed if Poisson's ratio of the material is v = 1/3. [4]