Experiment No (1)
PRINCIPLE OF ARCHIMEDES
This principle states that:
''when a body is immersed in a fluid (liquid or gas), its weight is
decreased by the weight of the displaced fluid, or in other words, when a
body is immersed in a fluid it experiences an upward thrust equal to the
weight of the displaced fluid''.
Theory:
Since the body displaces an amount of liquid that is equal to its
volume (v) then according to Archimedes principle:
Up thrust = displaced volume × density of liquid × acceleration of gravity
If the mass of a body in air is (M) and in liquid is (m), the displaced
volume is v, the density of the liquid is d and g is the acceleration of
gravity, then
(M-m)×g = v × d × g
(1)
The special gravity of any substance is equal to:
S .g . 
weight of any volume of subs tan ce
weight of the same volume of water
S .g . 
upthrus due to liquid
upthrus due to water
(2)
OR:
(3)
(note that S.g. is a ratio thus it has no units and is equal to the density of
the substance numerically).
From (2) we have
S .g . 
Mg
M

v d1 g v
(4)
(where d1 = density of water =1 gm/cm3)
if the body is immersed in water and its mass becomes m1, then from (1)
(M-m) = v
(5)
From equations (5) and (4) we have:
S .g . 
M
M  m1
(6)
Experiment no. 1A:
Experimental verification of Archimedes Principle:
Apparatus:
A solid body with regular shape, beaker, liquid of known density
and a balance, vernier caliper.
Procedure:
1) Hang the solid body by a piece of fine thread from the left beam of
the balance and find its mass in air M fig. (1-a).
2) Support a beaker containing water on the bridge over the left pan
of the balance on condition that the body is free to move.
3) Immerse the body wholly in water and find its mass in water (m1)
as shown in the fig (1-a)
4) Calculate the volume v of the body by measuring accurately its
dimensions using a vernier caliper. This volume is equal to the
volume of the displaced water.
5) Verify Archimedes principle from equation (5).
Fig. ( 1-a)
Exp. No. 1B:
Determination of S.g. of a solid insoluble in water:
Apparatus:
A solid, a beaker, a balance, and a piece of fine thread.
Procedure:
1) Weigh the solid freely in air (M).
2) Support the beaker full (3/4 its capacity) with water on the bridge
such that the body is free to move.
3) Weigh the body while being completely immersed in water (m1).
4) Apply the formula in equation (6) to find the S.g of solid.
Exp. No. 1C:
Determination of S.g. of a solid liquid :
Procedure:
1) Weigh a piece of solid in air (M).
2) Weigh the solid in water (m1).
3) Use the liquid whose S.g. to be determined instead of water and
weigh the solid in this liquid (m2). (fig 1-a)
Results :
Up thrust due to water = (M- m1) × g
Up thrust due to liquid = (M- m2) × g
Applying equation (3) we have
S .g.of liquid  
M  m2
M  m1
Exp. No. 1D:
Determination of S.g. of a solid less dense than water (wax) :
As the body is less dense than water, it will float on the surface. Thus we
must use a sinker.
Apparatus:
A piece of wax, sinker, beaker, a balance, and a thread.
Fig. 1-b
Procedure:
1) Weigh the wax in air (M) as shown in (fig 1-b).
2) Hang the sinker with the wax together, but lower than the wax as
shown in fig (1-b).
3) Weigh the system while the sinker is only water and the wax in air
(m3) as shown in fig (1-b).
4) Weigh the wax and sinker together while both are completely
immersed in water (m4) (as in fig 1-b).
Results :
Weight of the displaced water due to wax only = (m3 - m4) × g.
Applying equation (6) we have :
S .g.of wax  
M (of wax in air )
m3  m4