Leaving Certificate Examination 1960 Honours Applied Mathematics
Question 1
A mass of 
gm. is supported at 
by two light strings 
, 
which are attached to fixed pegs at 
, 
, respectively, the straight line 
being horizontal. If 
ins., 
ins., 
ins., find the tensions in the strings.
Question 2
Explain the terms “limiting friction”, “coefficient of friction.” A uniform ladder of weight 
rests with one end in contact with a rough horizontal plane (coefficient of friction 
) and the other end in contact with rough vertical wall. The ladder makes an angle 
with the horizontal. When a man of weight 
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
is a quadrilateral lamina. 
and 
. Find the perpendicular distance from 
of the centre of gravity of .
If 
is a point on 
such that the centre of gravity of 
is on , find the perpendicular distance from of the centre of gravity of 
.
Question 5
Derive an expression for the greatest height reached by a projectile in terms of the angle of projection and the initial velocity. A projectile, fired from ground level, just clears a vertical wall which is 
feet from the point of projection and is 
feet high, and the greatest height the projectile reaches is 
feet. Show that 
{-1}\frac{4}{3}
15
2
^2
35
30
1
224
4
1
6
^2
10
70
8
74
100
40
4
16
62\frac{1}{2}$ lb.]
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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