【物理科
PHYSIUS (2)
Suggested Solutions
(a) Law of Flotation
The floating body displaces
its own weight of fluid on which it floats.
Upthrus
of the floating body
wt of fluid dis- placed
where DD/S:
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Upthrust on brass = ()g
Newtons
院上
HALL
Upthrust on aluminium (7)e Therefore,.
Apparent weight of brass÷Mg-
Apparent wt. of aluminium
M'g M1g - M¤
Newtons
Since they weigh the same in water,
Mg(1 – 3) Mg(1
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bird, and is acting downward on the box. So it weighs the same as the bird is couching there. (iii) The upthrust diminishes as less water is displaced when a body is pulling out of water. It appears to be heavier.
(0)
The hydrometer sinks to a mark A in water, to a mark B in a liquid
of S.G. 1.10. to a mark C in a liquid: of S.G. 1:20 Let V be the volume of bulb' and the stem up to the mark A, and
v be the volume of 1 cm.
length of the stem... When floating in liquid of S.G. 1.10, the volume of liquid displaced is V-17, and is V -xv when floating in liquid: of S.G. 1.20.
Xis the length of AC.
of hydrometer = wt. of liquid
displaced W=(V 12.6v)1.10 - V
xv)1.20
V
12.6v
XV 12.6v.
1.20
12.6v
ilarly
12.6v
0.1/1.
X
24 28 32
Length 15 16 20 (a) Write down the extension for
each load:
(b) Plot a graph of extension
against load. (c) Define a law concerned with
this graph.g
(a)
Find the work done in increas- ing the extension from 1 cm to 17 m
(e) With the 0.3kg load on, what
force must be applied to Taxe pull it down until the exten- sion is 17 cm? What is the Potential energy of the mass? What is the totafhange
change in the potential energy of the system (spring+nase)? (f) With the 0.3 kg load on, what
force must be applied to raise it until the extension is 1cm? What is the change in the po tential energy of the mass? What is the total charge in the potential energy of the system (spring + mags)? (g)For what position of the 0 3kg mass is released from either value? Explain.
4. (a) A and B are two exactly simi-
lar spring carrying equal loads Each spring is extended by 6cm by the load L. (Neglect the weight of the springs as they are so small as compare with the load.
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The load on A is removed and the springBis attached to A. How much does A stretch when L is hung on B?
Whe
(b) If a body is totally immer- sed in a fluid, the forces act- ing on it are:-
(1) its own weight, and (2) an upthrust - wt. of fluid
displaced
If () is greater than (2), the body sinks in the fluïd..
If (1) and (2) are exactly equal the body will be in equilibrium, and will remain suspended in the fluid.
If (1) is less than (2), the body will rise to the surface and will
float partially immersed.
OI
0.015 kg
Lad
0:07.
When immersed in water, the stone weighs (0-025-0.015)kgf less. That is, the upthrust is 0.01kgf By Archimedes Principle, weight, of water displaced is equal to the upthrust.
The weight of water displaced is 0.01 kgf, so the volume of water displaced is 10 0.0.
That is, the volume of stone is 10ml
Specific gravity of stone is
0.025 0.01
2.5
The main balance reads more than 0,06 kgf. It reads.
(0.06+0.01) kgf = 0.07kgf
Answers:
(1) The volume of stone is 10ml (ii) S.G. of stone is 2.5
(iii) The main balance reads 70 gf
(d) Assuming that,
mass of brass block volume of brass block Density tor it.
M KE3 V m Dkg-m Mg N Mkg
weight of brass block mass of aluminium block volume of it.
m
it
of it
M'g N
in water,.
metal blocks are immersed
Therefore, MM That is Mg Mg
The aluminium block is heavier than the brass block when weigh in ai
VM/D ·MD'
since
V MWD M'D MM (proved) DD (given)
Therefore,
MD'M'D, M'D > MD;
VA V
That is, the volume of the aluminium block is larger than that of the
ass blondes Principle states
that when body is wholly partially immersed in a fluid, 1t experiences an upthrust equal to the weight of the fluid dis- placed.
The word FLUID is emphasised here, It is a serious mistake to replace it by WATER or LIQUID. This principle appli to both liquid and gas.
(i) Assuming that,
the weight of ice cube W volume of ice immersed Upthrust wt. of water dispa
density of water - d Volume of the melted ice.
En floating equilibrium: Before melting:
Wupthrust
After melting, the weight of that of part of water obtained from the melting ice is still weighing the same as before. Therefore,
W = V
·Va
Volume occupied by the ice cube. before melting is equal to the volume of that part of water converted from the melted ice Water will not overflow:
(ii).
As the ice melts, the immersed. volume diminishes and the exact volume will be taken up by the water converted from the melted ice.
(ii) By the Law of Flotation, the weight of the bird is equal to the upthrust of air on it.. Newton's third law of motion pointed that the reaction which is equal to the upthrust on the
0.2x1 1x12.6
#23.1
Ans. The length of BC 18 23.1-12.
that is 10.5 cm
S.g. 0.9
o 8v
Sg12
Let the volume of the solid be. V and density be f
Upthrust due to the heavier liquid, U (0.8V) 1.2
Upthrust due to the lighter liquid, U2 = (0,2V)0-9
Weight of the solid –
In floating equilibrium,
0.2 x 0.3V 16+ 3)
1.14.
Ans. The density of the soli
is 1,140 kg-m
Problems for the next week
In an experiment, the following readings are taken for masses applied as loads to a spiral spring; they are given in kgm., and the readings of the length. of the spring in centimetres.
0.2 Load: 0 0.1
0.3 0.4
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ii) The same spring A and B are now joined side by side to a very light lath of length 6 cm What is the stretch in Af the load is attached to the centre. of the lath?
6) If the load is now attached to
a point 2 om from the end of spring A, what are the stret- ches on the springs now?
(b) A beam of negligible weight AB
is hinged at A and supported at B by a frictionless pulley C and a stretched spring D. The beam AB is kept horizontal with the spring extended by 5 cm. When the loaded stone is put into water, the extension of the spring becomes 3 cm. Determine the specific gravity of the stone.
1kg
0.51
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