Junior Examination Papers, 1891. 
827 
EXAMINATION IN MECHANICS AND NATURAL PHILOSOPHY. 
Maximum Number op Mabks, 200. Pass Ncmbkr, 75. 
Wedimday, Koremher 11, 1891. 
{TJtree hours allowed.) 
1. State where the centre of gravity is situated iu the case of any two 
simple figures. 
Mention any one property of the centre of gravity of a body. 
A ring can just slide freely along a rod (AB) of uniform density; the 
weights of the ring and rod are equal ; where must the ring be placed that 
centre of grarity of the whole body (i.f. of rod and linc) may be five- 
. hths of A B^from A ? 
2. Define the moment of a force with respect to a point. 
Draw a square A B C D ; in BC take a point 0, such that B O is three- 
fourths of BC, and suppose that the square can turn freel}' in the plane of 
tlie paper about O; let forces P and Q act from A to B and from A to D 
respectively ; if P is a force of 20 units, how many units must there be in Q 
if the forces are in equiUbrium ? The forces being in equilibrium, what is 
the magnitude of their resultant, and along what line does it act ? 
;5. AVhen a body is placed on a smooth horizontal table and left to itself, 
what forces act on it, and what are the conditions of the forces being in 
equilibrium ? 
If the table stands on three legs, and the body is placed first at one point 
on it, then at another, what change is produced in the forces that support 
the table ? 
4. When is work done by a force, and how is the work measured ? 
Two bodies (to be treated as particles) are connected by a thread : one of 
them (P) is placed on a smooth horizontal table, the other (Q) hangs over 
the edge ; Q descends, drawing P along the table ; what forces act on the 
bodies respectively, and which of the forces do work ? 
5. In the last question let the mass of P be 20 lb., and let that of Q be 
5 lb.; if Q descends through three feet, what is the kinetic energy of each 
body in foot-poundals, and what is the velocity of either hody in feet per 
second ? = 32.) 
6. A body is partly immersed in water ; state the rule for determining the 
magnitude and line of action of the resultant of the fluid pressures on it. 
The specific gravity of a body is O'S, and its volume is 100 cubic inches ; 
how many cubic inches of its volume are immersed when it floats in still water ? 
7. Describe briefly the forcing-pump, and show in diagrams the valves 
(a) when the piston or plunger is being raised, (i) when it is being forced down. 
The plunger has a section of 36 square inches, and at each stroke is worked 
through two feet: the reservoir is 100 feet above the pltmger; find (a) the 
number of foot-pounds of work done at each stroke, (h) the force exerted on 
the plunger when the water is being forced up. 
8. Define the freezing and boiling points of an ordinary mercurial thermo- 
meter. In what sense can these points be regarded as fixed points .' 
Describe the graduation of Fahrenheit's and of the Centigrade thermometer. 
9. Define the mechanical equivalent of heat, and state its numerical value. 
The mass of a body is 3 lb., and it is moving at the rate of 1,000 feet a 
second ; what is the numerical value of its kinetic energy If that kinetic 
I energy were converted into heat {^c.g. by impact), by how many degrees wovild 
that quantity of heat raise the temperature of a gallon of water ? (A gallon 
of water weighs 10 lb.) 
10. Describe briefly Watt's Parallel Motion, and its application to the 
. steam-engine. 
