f)h\ ,,feot tJudntlth~ ·
l111d ~1o, 1'.u1un 1ent
, B'mitGiD
I
,h
, ,1~1,11h·r11,,n1 ,,r drmn,
11t ri1,•1,ul111
( l.lh 'i,1 I 1'\ll
•
\,11!,!, ,1,h,,
1, , , ;
'"1111 lh~l11111 "-
I I1111 I Ih
,•t ,ll'll\111
,,, ,,.._t;,111,1, ,. •lid, mr11H a
◄
I II Ill 11 1 li,111 1 ,,,
1 ,11 c I
1
\111111111
I
I 11111111111/1
\
\ ,.'!fl.'ltl, 11 "' iltlf1,1t , '"'"
df:'11\/tfi)~ 111
!h11•<1 Slft h'\ ,1/ 111M1t•1
I 1•111p ffli1•t1 ,,,
,11,
l111111111.11•
111
,, ltll·.... , .. ... ,~ ,
,h
1h Iii,·~Ill
11
ii, 1,•11,tl11, ti,, vulun11
l11r,:11l,11•,11lld111:11n )I
rllud, 1 I If
~1•1 •
l111\\'
1
, l\l,n, 1'> drJfllt111l11r• 1/11 \·u/11111(• 111 ,Ill l111•H1tl,11 \II/Id 11•,l1111, d
.' 111,•.'IS11d11~ ()'ll11d1•1
i Alnrc,101, ••Quired, A11 l1r,•w1l,u •,ul/,f (,r,y ,, pf,,,,, "I .io eJ,
r, P ,.
o1
ph•,
I',,, . ,,111g
11
write:, Ii 1 1lw ,11c:1,., 11 '"R I ylt, 1d0, 1111cl
,ccPrcl !lw /rw•/ 111 wo1,,, lwn, tl,c Hrnd1m1/on*
P,1111
so11 ti'
m"rkc•d on
/1,; WtJl/i;,
11
into tlH• ryllncl~, g1•11tly w11/1ou1 lt11Jtlil11g 11,,
WJI/~ o, 111(' h(ittorn, untrl /1 Ir; (0111pll.'tdy
'. r;,11,i J, 7/e Ilic
~t/111f: 11tour1d lho !.lo11c ,111<1
imme,~cd.
luwt1
11
11
~---
\\'I ' 111('11~1
,,,lid
• 1,
ll~lj
lth'1l ~IIII "''
1111 1111111111 ,,/
Iyll11elr•1,
"I
,,~ ll ti 1111,~~ '' "'
Ill
ti, mltl' '" ,, .r,lld. '"''" ht mu, and
lt ,111• Ill 1,, Ith ,1~111,•1I. II,, IIIIM 11( 1111y 110Jld C:.111 &,
\\11/i i/11 lwll' ,ii 11,l11•./i ,d l,1rl111l(, lh,vc,Ju.M
~,,/1,h, "" I,, 1111111d 1,, 111,1 11 f111mul11
I,,
(t'l llf'l't ill I !rt
· Pron,du, D:
dh
wuotl
Men~ut rrnr-111 ol <lc11~1ty of lrr11ul1r IOII
1
,' 0 llh..','ll>ll/lfllJ
11,,n,lfl'
\ 11!11 II It
, r,,1t~ll, 11, t1111I ~lr,li11 ,~
thn
,1,,.,., 1ly
il,,,1 111,11 ltt
ii, 111 ti, 11 11I
' " ' '" '"' "-' ,~ d1l1111d
11'1 l IIII \\ 1/,r I
11, ml11•
l.'t lfQII ·"
• f..-1,;til e <li,,thl( I
\
\\1 1;,11
I I
''" d, 11 .111 11I
llln.t~•,
• ~11-..:,1;rntm,·111 ,,, ,11•1" " '
•
l,c11
11l11t, 1 I
tl,,,11 \\t11til 1111 ,1 /\1\t 11 \11l111111, du II II fllllljlly It
11
\lt'hllf\'llh'lll
m1"N1\11fli\'l
t\ 111r 11~ "' '"'
111 l11
11 ~1, 1 ~,,11 \\
II
,,
I
.. ~-q..·· . ... .
u
..........
-_i\~~ V ~\f
/,
, d~t~rmii,e ti11.::, volume ot ,11, im:gul,11 sollcl u<,ln"
.., Eu. To
:: Ahn:
\I\ I
)
rJ
"
, c"'a 1..Jn
: "'
I I
/
. d An .irn.'gulJ1 solid (sJy J piece of !-lOm·)
:: l\btcri~ls. rcql: ,re
'
, J C.urcl-.a cJn, a piece of sll Ing
• a n1-.::-asunn~, cvl'
, in d l:I,
F ,.,c...·c ,11 ~•
su r ,. Fill the El.iref..a <.ar, with water.
(' ;. 5,...
:
j :.TEr ::i.
j
STEP 3-
Let the '" nter druin out from
th e spout. This ensures that
the water in the c.an ic; filled to
the point of overflowing.
Place the measuring cylinder
under the spout of the can.
Tie the string around the stone
and gently immerse It into the
can such that it doesn't touch
the walls of the can.
' ::.TEP 4. The stone displaces some
:
:
:
'
:
:
;
:
:
:
Fig. 2.2 I Measu, Ing the
volume of an Ir rcgulJrly
sh.iped stone using i1
t.urck.i can
: the streets shouting 'Eureka!
: Eureka!' (meaning 'I have
: found It').
l A Eureka can Is also called
water out of the can. Collect the overflowing water
into the measuring cylinder. Record the volume of
water collected in the cylinder.
' Ohservation and conclusion: The volume of the stone Is the
(V).
volume of water collected in the measuring cylinder
. - . - . . .. -
l displacement vessel or
.
Example 1 A mt·11s11ri11g cylinrlrr is Ji!!rd ,vith ,50 1!!.f of water.
.A solid with fllfTsscli, ~is thm l011 1ered into the' cylinder. The
u/rlter level rises to 58 ml. Detrrmine the clmsity ofthe solid.
Solution
---
Mass of rhc solid =
Initial level of warcr, V1 ""
Final lcvd of wJrer, Vi =
Volume of solid =
,
Density of the solid
i
16 kg
C
50 mL
58 mL
fncrcasc in rhe level
fj
=
V2 - Vi
=
58 mL - 50 mL
16g
= 8rnL
/\ I urr.k.1 c.m Is b.islc., ,lly
,1 conl,1l11c1 with ,1 •,pout
posltlonl'll below th<· lop of
the conl.ilric,. It I~ n;mwd •,o
ii Iler llw leg<•ncl of Ard1inwcJes i
whc>n hc- .1pparcntly :.tl'ppN1
into i1 public l>ilth, and rC'aliz<'d .
that the volllmc of water that
had spilled over was equal to
the volume of the part of him
that was in water. He then
jumped out and ran through
~er.flow~.
11w1t111ph: 'J, ,ii,/,,/,/ /1111/1 1/,, 111,t•, oj ,m 11111111,1// 111 /11• '/ 1.·
1/,i i/,, 11 1,1k,·1/I'll ,/II/, 1,l,'Jltlntl l/ftl/1 ///tr! J'flflly ;,!t{(n thrm
/ 111,, ,, / 111'f/.1,1 t ,/If
jtllrtl /Ill//, J/11(/l'I / It,
/flt/II'! fl//('/ //,1//IJ 1//Jtl I,
1,,//r,1rrl 111 ,1 11Ir,I, 1111,11, 1y/1111/r, !hr 1,w//m 111111'1/ 1lr111111 /""'' 1
1,1r,1J111ii1i: , 1,//111/,.1 1, 1) 111/ I Jr/111111111• //tr 1k11111y 11/ 1/,r 1,1111 fltll
Sul111l1111
M ,.,, 111 1111
V11l1111 111 ,,/
7 1:
111111 11.III Ill
Ill i11,11 11,tl, ;, il11 w ,11• 11~ tlw
111ll111,·,l 111 "" 1111•,,~llllllf: tyll111l1·1, ,1,,,1
I I ,,, I
I' fl!
V11l111111 "' 11111 ''"" II ill,
, Wh\l,, , t ,11 lh 11\ 1I11
v11l111111•
I llq11hl 111 11111•;,;, 11111111
P/l11nJ, 1, yr,u 11111\ I l"lt~lll t1
tl1;11 v1..1111 l'\'I I\ 111111 rd ht ti
I 11 •ii fllltl 111 lh li.l WII It Ihri li•Vl'I
,,t
I
'. ,,1
lltll
l11,11 1111 •
i~. ,, ''" "
()'},,ii,
I II
.I
I >111~1,y 111 ' III
7 y,
I
II 1111 ,
1
\'111111111• ,,/ Wil~r
1/,Hp/11il,
Mclisurerncnf of dcn,;fty (}f llqufds
llq11hl
l~ v, ,y ' •"Y 111 d, ·1r 11,d1w rl11 ,I, ,,.,,,y1,l ll,p1id~ ,,u
1111,q,,ut: J 111 !11,11 11/ ,11l1d, 111 /',·'" ~ llw 1111,s'i" 111 J liquid
l1
I,~, 1111.:,1•.111, d w 11l1 dw lwlp ,,I .1 pl1y1il1 ,,1 l,,,l.1111 c and dR
v11lt11111' , ,111 l,l 1111 .1,1111 d wid, d11 111'11' 11l 1_1,1111l11111t'd '-')'Undlil,
I ,·111~ 111tl,11111 ,111 ,11 tlvi1 y 111 ,I, 1, 111ti111• tlw d!'ll ,i1y ofa
~,,11
1
lltjt111I
~
\
I
I
I
.
3
'Vw
•,rr
I
( 1 1t
f
1
l\lnil 111 drlt•1111i111• l111• d11 111,ll y 11111 lhp1ld
Mnt (:1I,,, I "f1lll1111 II i\ llq1 lie I, 1 1111'11' 11111 I►( ' ylh I( lt•I, I11 ,y,, I, ,11 I1,11,II I( fl
I
' 1'1 vtetlrn 111
• 11 r " I !IHI tl m 111.,~~ 111 1111• 1•111p1y, ylllulc, Willi thu l11•lp 111
1111 pl1y1,h Ill lt,11,11111·
; ~, II' ~. I'11111 I111 1 llq11lcl '"' II I1111 I111111>,111 Ii 1/I I yl111d1•1 ,II 11 I
d1•1 r 1111hu1 It \ 1111a J ,1j,!,1h1
\
, ~" '' \ N111 1,1 d11w111111• 111,11k 111 will, 1111111 llq11ld /Ill\ t/ 111
11 ,, , ,I 11 ,,, llq11ltl I•. , 111 Vl'd, I111•11
i ylll11lr1' II I Ito ~11111
tll~ 101111111g d~•111' IHI\ 1111 111,, I IIIV1llli11' ,,, lilt• llq11ld
(11111 i,1c111,~11\), II lho 'i11vn 11111,, 11p, 1111•11 ,,,,111 ,1i,,
tit,• 1111•11lr., II~. lt11w,,y,,,, I( 1111• 1IIIVI' u,111«
r •
I
I
!11p "'
ti
t 0Wl1, l 1,·11 tt'ittl 11t, li1,1t11111111 lit~ 111,·11h1 II~,
Ohw1vittlon 0 0 ~ 13u0111
' Mll\t uf lhtt 4:lllplY lyl111d1'I • 111
Now
,
M
I
'
1 • 'zi
H\', ot t "' llij11ld, Ill
Vvh1111c Ill 1h11 llqt1ld
t>tnshy ul lhl1 llq11ld
1111\1(! /',!JP.
d11w11wnrtl•
1lfl, ,,,
I Vol11m1
oM,,r.r, ol ll1t• ryllmh•1 lllh•tl with liquid
111~ 111,
~ vJ ,y~ ~~
111/V
~"'
.). ,, J
\M~ '...1\..., ''""
,..,o
, __,.' "
Write
2..
.
bilse.. Correct the ta stace,e-cs..
The density o f ~ soids Gin be- d!tti ~ 'Mlh ft bi$ cf~ ~ ...~ - , The drop in the~ of~at« 1n a ~ c,in,~ ~ Mt Clb.Kt ~ dt ~ ~
,:
Y'Oksneoftfle.otJiect. •
true oc
-
__ 3- _A Etreka can lS a ~ wich a sp0\,,"t ~ Its bo(cora. ~
. .
.
··- ·••·-··· . .
Relative density
From Tabk 2.1. rou will find dw ~ den.sin of ~wnin.ium
is kss dun the density of iron but more mm tlw of~ In
other words. we an ~- that .aluminium is lighttr dun tn..-'\(l
bur hca,ier mm i~ fur their ~u:il ,-ol.umcs.
It ~ill be pracrially impossible fur us ro mcmomr thtdeo.sicy of och m.areml ro comp:ire its dmsin w th .anodlcr'
rnceri.2.!. In order ro a,'Oid such ronfusioo. s c i c n ~
che densities of mosr suhst:lnccs co ~ dmsirv of wan•-' ec_
This is c.alJed the rdam-c dfflSi~- of 2 subst:ana["'DM. I , , -.
$ !..iti
ol dlt
of a subswicc is ddiocd as the mio
deosin·
....,_;~
_ ___
-~--------;..;;.;;..;...;,:._
of the substance to thecfmsft}
renn used for rdam-e dcnsio· is
of-...uu ar 4 °Q
spccmc gra •
_ . . . : : : . -___,,j.......' ~
R.dativc density of a subsantt. RD = _____.,...,
Drnsio· =
·
and
Yt-artt.
RD=
~
Yolwne
, so
for cqml volumes
dx rdative density of the su11-.
Mm of• mbanoe Ma ,Ii
Volume ofmt sublaocr
Maa ofme mbmocr
= Maoiwam114°C
~ uladw de, 1
defined ~ die ndo of.
--••
la
-
a:laaiwt-«wi:; alJX.cc:IS:~"''sa ma
~:::
F-
II J
~~ -
~Ga"~~ -
~~--~
~~ !tJ!>-"r ef,:z,JJ, ~ " 'JUE if 411r.._
3001t"Emi.tz:~ iDIZ~~
SI •
, .....•,T
,~
~cfo...~ = _;~- =
.
~~
~~
:::
~$.-.-.
- ..-~RD .._,r.-..urE = ~ ; - ~ · -..
flet.ltM. d&ay bottle
. •- ~~~
Tur~
.
~ "'-ictk
. ~is~
1he~~N
L--
-
IS
~-
Sblff'(f 1.W'~ J. ~ ~ - - - ·
L-.:-
.bidi i s ~ madi:d on me
me boalc is complcrd! ~ ·
inserted. ~ c:u:css &q.f mes
and dams OU(. This
afiml~~aBT
dc,mnin,:
•
me dcmir, J
......,
cls-,d~llpd-.~,__ ._l:,Ji
. . . densilr~111111td!dtd..-,.Oryl.._
usilC dr 'bit -i
lll9_,_. . . . . find Is - - ~ - . illl!alll wallr. -.t dlt stist~•a_...:1
. . . . . if.
F'
STEP
~. ind the rnass of th b
.
ST'Ep s. Empty th b
e Ottle filled With distilled Water.
•
e Ottle and dry it Well F'II .
.
1
determined and insert
.
·
,t w, th
whose
relative density is to be
t h e stopper
r the
'd liquid
.
.
50
1
bottle well f
·
me rqu, w, I drarn out through the stopper. Dry the
ml ation:
o~tside. Find the mass of the bottle filled with liquid.
., Observation a n d carolcu
:
Mass of empty bottle ::: m
Mass of bottle + distilled water :::
m:
l
Mass of bottle + liquid == m •
M
.
3
ass of distilled water :::: (ml _ m,)
:
,
Mass of liquid ::: (m - m,)
3
As the volume of both the liquid and water
are same,
--
RI
. density of the liquid = m -m
e at,ve
3
1
m2 - m1
3
Density of the liquid ::: m-m
' x , g/cml
£;,:;~•:o:;::::':
.
ml - m,
:
0
~ : ~ ; : : :•~,,: : ~ : :
0
:::~•-help_of a'~'.~~~~-~~~';".."~".'•·_... .'
filled u i rh u•ater, rhe bottle has n uvm of55, 7 5_Jf nnd ,45.l!Lt;_ _
wh,m filled wfrh alcohol. hud th, (;) "?/um, ofth, bottle. V
(H) RD ofalcohol and (,;;) dmsfry 07,ol .
.-0 ,
r. --,.
~
Solution
mass of water" m2 - m,
= {55.75 - 25.25) g = ~0.5.0 g
As the density of warer is l g/cm3, so the volume of wacer
rn
. rh e b one
l IS
. 30 • 50 cm3 · This means that the volume of the
borcle is 30.50 cm 3.
Mass of alcohol = ll13 - 1111
Thus,
So,
"'J
RD of alcohol = -
-m,
"'2 -ml
=
rlhus, che relative density (RD)
Density of akohol = RD of
= 0.66 x
~Thus, ihe density of alcohol
•
~; \
..,\,,-"" ~ ~
(
\ j ~~~o
J\fass of empty RD borrle (m 1) =- 25.25 g
Mass of RD bottle filled with war« (m2) a 55.75 g
Alass of RD bottle filled with alcohol (m,) a 45.50 g
= (45.50 - 25.25) g ;= ~ g
3 o-- ::,
~
\)"O'l,Y" ~
-?J .;y,,\»"
{
,\. ../~ .. J
\~
.d
'6
.-,,;,·
v~
V'-
\.
i
~ttr
Ah.ydrt.lftWttt l,, •~ '"-''™'"~'• \hf\l 10 m, ,,u1t' ch<'
1., \l,u.alh m ,,1, ,,t ~I~'-~ .-nd , ,,mtaa
dmait)' ut
Uq~,,
htff
• lvllndrl\-il ~\tm 11Uhl • t,utb ,,n hm_l\\Uh nu·t\\lt)'
~ to n~r u t~t upr~f lht· l,,1m,I w hr lt'st\"\f la
1ntu j t.tll t,r.•o,d th(' hhhvmun I\ ~\'tll h lo,,'\"l'\"\l lnto
hqtuJ unul tl H,,u, freth l 1._,,w1 th<' d, n,1t\ ot a !tUDnW&:
tun~, "ill thr h,,lmmn\ r !\tnk llw 1x,it11 Jr whkh the
~urta'"" oJ 1hr liq\UJ h_l\td1r, the- srem ,,t 1he h"!romnw la
n,1tf\i \{:lnll\J.IH\'h ~ U)U.llh "'myin J l\JP<'f ~"illc-1aaldt
th<' \l\ m that ,, \llt.\l 1c, lt'.h_l thr rd,.u ,w ,ku~ ~
! h,~1\,mrtt·1 ,, commonh usC\I 10 ll'\l fht' purin of mJI.:
'" '' I A hydrom.,~
lh1\ lmimmrtr-t
I\
\''.;tllc·d .- l11l'111mttu.
Flotation and sinking
Gi:J,C'n .l "olid ,, pla'"'t\i tw~t • hquid. h ma
I
,•I
Tht ~•ti~ <MntJty of a
~ubstanct (or
tJJJ
know wh4tthet'
~/ .,.,p,
1n ~ )
us to
wlll
I\
Roat or link In W1tef
• ~bst1nc.1 heYlns ...i.ttvt
dtnuty lffl thin , wll
float Ol'I ~ aurf1et of
Mttr. For•~ WOOd.
t ~ ktrOHM, ~
ol11nd IOOI\.
•ThON~l'NHYt
dtnslty mort than , _. In
waw. Fer eump1e, Sold.
lroQ. llumlnlum, a3PP«
Ind IO on.
ll('()Cml111g on ,hrlr daltica.Jf t
chan ,he dc1~1~• ol the llqwd.1.
l,quid It 1he drnsi
the: liquid. 1hc ob
A solid m11
deprnding o
!,inb in w.trt'
".tt('r hur si
lfrwo
gn-.1ttr
'
[
I
~ - Since river \: 1
;-. ,uer \,\s lower 1.k1 '
' · m l. l,\11 s~-.1 ",th•1•• t ship
loade-d "ith . ,, . l
.•
C,lr.:,O ~u 'lllt'r•• ,, t
\l~)t<.: in 11 '1.'t \\,111.•1 tlu11 in
~1.
.
se,, \\;tter So l
· '- 'tie \\e1"lu of ti,
1i.1, to b1.• lmuh.-d tti
• 1., ot~ \ ,hi 1 .ti.: 1.,ltgo
prevent thI.'., Stn~n,,
.
• • . I in rt\er \\,1t1.·1. Foi tlw 1',mw
b
.
rca~on II s·Iltps
e 1n k·
ht,
' ,l
,lr mgi. on thd1 hull t1.) indk.1t1.•
' '
the I . l
.
e\ie up to which rh, .. l . l
t.:\ t,\11 )C' ,u 1 11\1.' rg,1.·d ~;\[c,:h in ,I
~
1. •
p,trticuhr sea or riv , 111
es1.• nur~ng, ar1.· 1..dkd f'lam~ohii
<.:r.
·
r•ne$. If ~, ship
~ •
1 •
is lo1d •·1 1.
• • <.:u oeyonu 1tl'> l'limsoll lin~-. ir runs
~- •
h
__ '\
tC., t e ns~f s1nkinet.
.
•
~
~
------- ......................... ········ ..... k.:i..
~@li W'il@~
.:
.
.
Fill in the blanks.
,
3. A
:
.q. Kerosene will float over in water because its density Is
:
5. The density of sea water is
'
1.
A wax candle
u'I \ "Q~
on water.
2
•
The raDtio of densi& of a substance to the density of 'vvater at 4
of the substance .
i... )
1-l~cl~,
tr\J. •
lf.'~ · ~
"J
&,
cooling. For a substance having ., fixcJ mJss. the_ dtnsit~· will
change if the volwne of the subscan<.:e changt•s~1t•;~_!l1.11
if the volume of a fixed mass of a .substan<.:c dt·crcascs.i..Jts
- density will increase whereas, if the volume increases, its
density wilfdecr':as~.)-
-
tha11 th::it ot
than the density of distill~d ,vat~r.
In genera10;acrer expands on he.Hing and concr.Kts on
-
SoJids do nor undergo significant expansion or contraction
with change in their temperature. & a result, there is no
significant change in the volume of a solid when it is heated
or cooled. So, rhcre is almost no..:c:bai:lp in its density.
~•~change
However, in case of liquids
,Aa
in their vo Iumes even WJ'th
a resul,r, when a liquid or•
ad when cooled, its d •
of ditfurc
::i, the
is the instrument used to measure the relative derhity of ltquid,.
Variation of density with temperature
-
•c I!> l..nown
@
WJt~I'.
'
.
''
Hul.W Huld.1 txpan<I on h
•r-nilun, 1hr lkn~hv of 1hr hc11tNI pottlOI 'fl.
d«tt~, .-.n,1 h h<'1.,omts 11~111, Warm Rulcl.
Jc-lUC' 110,l h~lncr,V't~ ui,wa~lhe cool,r·DOn•
tht. Auld, lx-tnt' ~omfltlr1111\1Cly Jrnst'r and
Jownwinis 111,d 04;,upit"s ,he spucc cmued by
tmwtment of, h(' ho1 Huid, If hear ls suppllocl
the rntirt 1.yde of hOI fluid rxp:anding nnd
followed b)' cold fluid moving downwnrds IO
\'Omn\\\l\ly lAll<"i
Mil•
~'Of\Ul\ll~,
·rhis consranl upWl'Ud and.d.ownWtrd circ
furms currrnrs in che medium called conwcd
" -.,, Is the toallng unit of
• r-ef-.e.ltor fflldt at thf
top?
a wtfl/ 11 an ~
norfflllr NUiied at •
hllfltlnlroom?
Convection currents distribute the heat thro
of the AuiJ. Air is a mixture of gases and the
curn-ncs c11n be ,cc up in air :is well. Natural ph
.is land .md se.1 brce7.c~. monsoon winds and tht
associat(d with convection currents arising due
heating bctwttn land and water surfaces.
Comparison of densities
in the three states of matter
We know that the density of a substan
quantity of mancr in a unit wlume.
•
unponant&aoa afecdng the