Applied Mathematics

100 marks · 3 hours · 2 questions · official PDF, 2 pages

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Applied Mathematics · all years Q. 1 · Forces of magnitudes P, 2P,…Q. 3 · (a) Find the angle between…With this paperOfficial PDF2 pp ← 2022 2024 →

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Q. 1

(a)Forces of magnitudes P, 2P, 3P, 4P act respectively along the sides AB, BC, CD, DA of a square ABCD, of side a and forces each of magnitude (8√2) P act along the diagonals BD, AC. Find the magnitude of the resultant force and the distance of its line of action from A.
(b)A uniform rod AB of length a and weight W is freely hinged to a vertical wall at A and is maintained in equilibrium by a light string of length a fastened to B and to a point C at a distance b vertically above A. Prove that the reaction at the hinge A is and find the tension in the string.

(10)

Q. 3

(a) Find the angle between the surfaces $x^2 + y^2 + z^2 = 9$ and $z = x^2 + y^2 - 3$ at the point $(2, -1, 2)$ .

(b) Show that $\nabla r^n = n r^{n-2} r$

(c) Find the total work done in a moving particle in a force field given by $F = 3xy\,\boldsymbol{i} - 5\,z\,\boldsymbol{j} + 10\,x\,\boldsymbol{k}$ along the curve $x = t^2 + 1, y = 2t^2, z = t^3$ from $t = 1$ to $t = 2$ .

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The 2023 CSS Applied Mathematics paper set by the Federal Public Service Commission. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet. Open the official paper beside the questions to check any of them.

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