760 
Junior Examination Papers, 1892 . 
EXAMINATION IN MECHANICS AND NATURAL PHILOSOPHY. 
Maximum Numeer of Marks, 200. Pass Number, 76. 
Wednesday, November 9, 1892. 
{Three hours allorced.') 
1. Draw a square; suppose that particles are placed one at each angular 
point, and that their masses are 2, 1, 1, 1 respectively ; show the position of 
their centre of gravity in the diagram. 
If we suppose the square to be a lamina of uniform density and that its 
mass is 1, show, also, the position of the centre of gravity of the whole. 
2. Draw a triangle ABC, with its base A B horizontal and C below A B ; 
let A B = 6 in., B C = 5 in., and C A = 2-5 in. ; let A C and B C represent strings 
fastened to fixed points A and B, and carrying a weight of 90 lb. fastened to 
C : find, by a construction drawn to scale, the pull which the weight exerts cn 
each of the fixed points A and B. 
3. Describe briefly a pair of toothed wheels working together on parallel 
axes, such as may be seen in a crane. 
If the driving wheel has seven teeth, and the driven wheel (or follower) has 
eighty-four teeth, how many times must the driver be turned to make the fol- 
lower turn five and a half times ? 
4. In mechanics, when is an agent said to do work ? 
Putting friction and resistance of the air out of the question, would it re- 
quire an expenditure of work to make a body slide with a given velocity along 
a horizontal plane, and if any, for what purpose ? 
If the plane were slightly tilted up, how would this circumstance afiect the 
answer ? 
5. What is the name commonly given to the force which in one second 
imparts to a mass of one pound a velocity of one foot per second ? 
What multiple of that force is the force which in 3 seconds imparts to a 
mass of 12 lb. a velocity of 20 feet per second ? 
6. State exactly the meaning of the letter g, commonly used in books of 
dynamics, and what is meant when it is said to equal 32. Is this number 
exact ? If not, give a number that is more nearly exact. 
7. If a body fell freely from rest, under the action of gravity only, through 
a distance of 300 yards, how many seconds would it take to fall, and what 
velocity would it acquire 7 (y = 32) 
8. Define the specific gravity of a solid or liquid. 
The specific gravity of alcohol is 0-8 ; that of olive oil is 0 92 : how many 
pints of the former would weigh as much as 3 gallons of the latter 7 
9. State the relation between the volume, pressure, and temperature of a 
given quantity of gas. 
A certain quantity of air is enclosed, and is found to exert a given pressure 
when it has a given volume and a temperature of 0° C. (absolute temperature, 
273°) ; it is allowed to expand slowly, and is found to have four times its 
former volume, and to exert one-third of its former pressure : what is now its 
temperature measured on an ordinary Centigrade thermometer 7 
10. Six million gallons of water go down a fall of 1 1 ft. in every 24 hours : 
what is the horse-power of the fall 7 (One gallon of water weighs 10 lb.) 
