# 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}152^235301224416^210708741004041662\frac{1}{2}$ lb.]

**Citation:**

**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/

**Licence:**

**Licence:**

*“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.*

The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).

Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.

**Links:**