BABSc, B.Com & BCA Questions _III - Nalanda Open University

9. (a) State and prove Poisson's equation in Cartesian form.
(b) Prove that the cylinders x 2 +y 2 -2 λ x=0 are a possible set of equipotential surfaces
in empty space but that the spheres x 2 +y 2 +z 2 =2 λ x are not. In the former case find
the potential as a function of λ .
Group-D
10. (a) Show that the pressure at a point of a fluid at rest is the same in all directions.
(b) Three fluids whose densities are in A.P. fill a semi-circular tube whose bounding
diameter is horizontal. Show that the depth of one of the common surfaces is
double that of the other.
11. (a) Find the depth of the centre of pressure of a triangle immersed in a liquid with
vertex in the surface and base horizontal.
(b) A hollow cylinder by a plane base is filled with liquid and held with its axis
vertical. Find the resultant horizontal thrust on half the cylinder cut off by a
vertical plane through the axis.
12. (a) A body is entirely immersed in a liquid being supported by a string. Find the
tension of the string.
(b) A mass of fluid is at rest under the forces
X = (y+z) 2 -x 2
Y = (z+x) 2 -y 2
Z = (x+y) 2 -z 2
Find the equation of surface of equal pressure and curves of equal pressure and
density.
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