802 
Junior Examination Papers , 1893 . 
EXAMINATION IN MECHANICS AND NATURAL PHILOSOPHY. 
Maximum Number op Marks, 200. Pass Number, 75. 
Wednesday, November 8, 1893. 
( Three hours allowed .) 
1. If a body rests on a horizontal plane under the action of gravity, what 
are the conditions of equilibrium ? 
Suppose a body is placed on a horizontal plane in such a position that the 
conditions of equilibrium are fulfilled, what other condition has to be fulfilled 
if the body, left to itself, is to stay in that position ? Illustrate your answer 
by the case of a ball so loaded that the centre of gravity is not at the middle 
point. 
2. If a body rests against a smooth point, in what direction is the reaction 
of the point against the body exerted ? 
Draw a line AB, and suppose that it is inclined downward from A at an 
angle of 30° to the horizon ; take in it a point C, such that CB is a fourth of 
AB ; suppose that AB is a uniform rod supported by a smooth hinge at A and 
resting against a smooth point at C ; show in a diagram the forces that keep 
the rod at rest, and show, by construction or calculation, that the pressure 
of the rod on the fixed point at C is very nearly six-tenths of the weight. 
3. Draw a diagram of the first system of pulleys (in which each pulley hangs 
by a separate rope) with four pulleys, one fixed and three movable. If the 
weight is raised one foot, how many feet must the power descend ? What is 
the least length of rope that must be used if the weight is to be raised one 
foot ? 
4. What is meant when it is said that the coefficient of friction between 
two substances is 03 ? 
At what points is friction exerted in the case of a cart-wheel ? Explain 
why it is easier to draw a car along a tramway than along an ordinary road. 
5. If a force of three absolute units (poundals) acts on a mass of 10 lb., 
what velocity does it impart in 1 second ? What velocity does it impart if it 
continues to act for 7 seconds ? 
6. What is the kinetic energy of a particle whose mass is 12 lb., and which 
moves at the rate of 15 ft. a second ? If the motion of the particle is resisted 
by a force of 9 absolute units (poundals), what will be its velocity when it 
has described 20 ft. ? 
7. A glass ball weighs 10 oz. ; it is found to weigh 6 oz. when it is in a 
liquid A, and 5 oz. when it is in a liquid B ; what ratio does the specific 
gravity of A bear to that of B ? 
8. Put a piece of ice into an open tin pot and let it half melt ; then put 
the pot over a flame ; of course, in time the water will boil and be evaporated. 
At what stages of the proceeding will the temperature of the water be 
constant, and at what will it be continuously increasing ? 
What difference would there be if the process, instead of taking place near 
the level of the sea, took place at the top of a high mountain ? 
9. What is the relation between the volume, pressure, and temperature of a 
given quantity of air ? 
What is meant when the coefficient of expansion for 1° C. is given as 
0003665 ? 
If the volume of a given quantity of air is 10 cubic ft. when the temperature 
is 20° C., what will be its volume when the ^temperature is raised to 21° C., 
without change of pressure ? 
10. A fly-wheel weighs 20 tons, and we can suppose the mass to be dis- 
tributed along the circumference of a circle 30 ft. in diameter; if it turns 
at the rate of 40 times a minute, what is its kinetic energy in foot-pounds ? 
(y = 32, 7r- = 10 ). 
If it had to give up 800.000 foot- pounds of irs energy, by hovr many turns 
a minute would its velocity be reduced ? 
