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### Maths Grinds' Blog

Blogging and Mathing
20 Nov 2018
##### Question 1

A mass of $21$ gm. is supported at $O$ by two light strings $OA$, $OB$ which are attached to fixed pegs at $A$, $B$, respectively, the straight line $AB$ being horizontal. If $AB=7$ ins., $AO=3$ ins., $BO=5$ ins., find the tensions in the strings.

##### Question 2

Explain the terms “limiting friction”, “coefficient of friction.” A uniform ladder of weight $W$ rests with one end in contact with a rough horizontal plane (coefficient of friction $0.6$) and the other end in contact with rough vertical wall. The ladder makes an angle $\tan^{-1}\frac{1}{3}$ with the horizontal. When a man of weight $6W$ is one-third the way up the ladder, the ladder is on the point of slipping. Find the coefficient of friction between the ladder and the wall.

##### Question 3

State the theorem of the Triangle of Forces and its converse. The perpendicular bisectors of the sides of a triangle are the lines of action of three forces. Each force acts outwards and is proportional in magnitude to the length of the side to which it is perpendicular. Prove that the three forces are in equilibrium.

##### Question 4

$ABCD$ is a quadrilateral lamina. $AB=BC=5″$ and $CD=DA=AC=6″$. Find the perpendicular distance from $AC$ of the centre of gravity of $ABCD$.

If $X$ is a point on $AD$ such that the centre of gravity of $ABCX$ is on $AC$, find the perpendicular distance from $AC$ of the centre of gravity of $CDX$.

##### Citation:

State Examinations Commission (2018). State Examination Commission. Accessed at: https://www.examinations.ie/?l=en&mc=au&sc=ru

Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/

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