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NOOK WHF Buscutiy i » PraysiceD quality — can be mupiivud by cur mebupunt o Neon - ply sical quontiny — con't foe mean real by en inebrumert 4 a Physical Ouucwttiby : » Furclowmuuntol [Bosic Quantity. (4) 4 these OH imclipeneled y each stunt que furclomantole (Heese wzloutol be univeual aceeptrnes Fa aks should be ery. Gi teow oot only 7 fund ta) au i ; x Laur 2 Ae oO { UNITS 2% DIMENSIONS % Moan Kiteqram (3 ) ; Cm] 4 lenate mute Cm) tv) a gecena (s) tr) ‘ _ p Kelvin («) (k] » [le] 4 Curiient Reapers (4) tok " Amount hh substance mole (mel) [mot] Luminew, imdensity Conolela (col) Kal " “4 Supplementary Bruprctity cz ‘ Raootitey | aia Dimension a Plane angle (6) Rowtian (rad) Ki «oul ~ ; ~ Solid Fmae ra 2 une (<°) Di . i‘ =) ay hy ° Plows Fragle ma) Are = Rody * ise ot a endre fre = RO . (C) B B = Are [ “| ST unit + red — ee @ Solid Pnsle (2) : “2 = fea J] > Prea — AA - Re Sr uit —> storadian i i § Find out solid ample msl by sphowt ak sa" = fren = ATURY ¢ ~ Re Rez c : Na ph dosh ‘ (Cominuk) 6 s g 4% ) 60° 2) 45° 3) 180° 4) 360" q us rod 46 a Tuto: 27 rod ® ZE\ vost &) ' & Cond Lwimate f into odour. q od eo" 4 = 60! ql< (i) . ae i lor = (oy Bod = Se nn) 180 19800 r= x red 130 ‘ =]2-4 x10 redion| ty "Young's Modulus (Y) = Shes = MT = Per Strain meiet ° r ay? _ es a Energy Desi = Showy = mt = [me Tv ] Volume a = beer = 8, 2 pe = | y sheas X sain 2 _ _ [rey Si ac 7977979448 © Cuorge ¢q) = tt = (at) © Electric potentiad (VY) = Wo = MT e =[mir Ta) 4 AT | ®@ Planckxk eonstant = Emngy = meer = [mutt] q Frequancy TT | * Gravitations! = _Fre = (74) Ce) = {mist Contour meme ~priem) @ Boltemann comtant (ik) = Egy = 22 e *Viswsity (Ws ee aie ere Y= ~F Ax = (mrrjCe] = [ues ~] “Av A Foye) aS W al’ 4)7 I 3 7. i} 1 2 | A , os | CPPPPPPP? © Ruorpout Tension (s) = Force a [M72] L Femgth *— =e = [ir] o Refractive Inslex (n) N= Co = ur « ( oe Hair 7 ur} Cmditim = olimentiontsa (wer ] AREREN x meg FF APPL_OF DIMENSIONAL FoRmULA i ~ kKupw the unit be gives ctuawtily * Principle oh Homogeneity BS Estab stunt §}) ratation Arwong clit. quantities ~ Suoit day | Cowersion » Units from ony system to anther dyrten, mee FTE Know tee Orit of a quantity = may * StS = fer] = met om mis ® Accs = (t?} oo sence = Qoert] = by let or went) a] "Wok | Enertay = {mv 17] = ky m’s* or Toule (x) way . 4 Principle of Homogeneity +~ ail youre oo out + bar mi fo) = Gr) + ty) = Jey + Eyer ry + for + firs] ; “ ae eae mew ty ~) | Sort ee ee mR wp. 4 4 Punure P= « "a P= (& oat erg 7 ~ =e / sti) BE a were, pe ee = WD * p be = of be} Gi) xe = Ts er: v2 95 feted pw BO (met = {{mt‘] f & 4f x = A sin (cot + ky), wth mye t ane aictances A tine susp: Poth bE 4 w, kK w A. ~ ~ ab eet oN x=A sin Coot + ky), tot + Ky = [mer] =L = => w= tL tot = 1 “3 ky = 1 & Reledi enshi p Prana bit: Dwoodtities — a) a mos (my KR acer (a) tukim 0% “fuvclouatita) quavditiea thas Pru vill be = or ce dlpencl m ‘m' tal Lt kon formule he ise se F xkm* of fury = 8 te bol! wou kK = usted = [mover] Sxperimentely , Kel éb) 4 acc® due to qrevity (4) , Wright (hy and mart (mm) osu fordomintal quantities Hen potential energy cw) Sol" “a = gh? m* yea a ee) 4 wieés 4 are Se" i - h’ eG Ferclomerdat Phun C ny ery i [im ut aa = {w**] {> ry +3) [1 -4 1 { sep = Dey cat et — © tre bee ou, mt ax ty t seat -x -4-22 =0 x yor ox a4 ~Sx-y = 0 x= Zz x44 =0 47 Tl tahoe 4 ees zat y= Le ng hes CPPPTTIVIFTVLTAUR BIE a [=| [sey ay? = 10x oy) = \ot 0.24 8B Lp = Wem M, = 100g Lowevrion > 4a fems 2 Ag ems -f ms GE) Ge) (@GR) > ACEI 9 Pytd ik lL = (01m M, = Olea, “T, = tminw + 60 see Comewien , 45 = an) = (5)(ae : ‘g ms? Cm y-2) yh i_\2 _ ( | x 3 66 — enw hh. >= Sut fn NRW arpetem tant lengths mars KR Hime cote Xm, p 4 and Yrin- Than JOT” will be ; lL, = , 1% = Ymn = GOY see n, = Io [ko] fit ye fs 7? 4 T = Mitt BK xm 60V # 2 Wo plo * 3600 ¥** ne = 36000 a Bx” 4f Im a new miganemn 2), tig, Magy x Wiles «ime aes om , Bk , y mins Then, im this new system of unit , loys ane equols to neaX pty een volute % n+ x + yrs ys = ai wT = seo0oy* = BLOOO * BY * x? B n+Re + Pte = seooo + Gey + (-1) +12 = [55599 | = Least Count = (tc) ‘eost sunt an wstument ye thed win. Baecetae ty moriviesl value chith con “be measured by vt cenat Court 5 Verwier (obtipes — le = 1Msp — AYSb ) te = 1 MSD Totel no b divisions on vernier scale (V8) - Zew Err Ze Enron of VC VO ) No futo wvror @® Positive fo} o 7 mis. lool \ MS triplets pot oe ql oO i) ° CO ’TZ_ WAL )eaem << bee ] E Le_DF_ SCREW gauge Lmcromerer - es. “me precise tor smaller ~ Peanslingg t = Pitch EA msn) — —— Total ow. divisions of circeclon scale stud jour douse MAT, sales aie) time t Zeno error of Sere esas = 'o’ visible. ms 'O° invisible Ni “we i “a y NS Fre Evrer | Cb) Positive eo error | (e) Neg ative Gero exrer | ‘ Oo —fe o-Es \ of ts 40 J Reading =-fase + csr] =S (ce + 02 xs) — (o+ o-1) = 0 + (tt xo) : = 0 + (002 x5) | = oem = oto | —_—_ ave ZUAIw YLLEr Reading = MSR + CSR Reading = “SR + EsR =o # LOX = 0 + fle xm) | J = 0lmm | coinciolinp nth will be counted from ‘o! of CS — thn +e Zero evior [0 of es is belao 0 of mg) ES SSS =—=>——- ~ ow Road & Compettive Exams (Lovel-t) Nor on Units and Measurements 41 41 The volume of a cube having sidas 1.2 m is 47 appropnately expressed as (1) 1728 = 10° cm’ es « a) ana wy? ~ 10 cm 288 « bY x 43) 18 < 10° cm hae * y \4 2 ® (4) 173 *10° cm 42 An odject of mass 4.237 g occupies a volume 48. 4.72 cm’, The density of the object to appropnate significant figures is U2 46 g cm (2) 2.463 acm” (3) 25gem? (4) 2509 cm> “\pased on Experimental Skills. Vernier Caltiper The dimensions of a rectangular block measured with a vernier calliper having least count 0.1 mm is 5.0 mm » 10.0 mm » 10.0 mm. The maximum percentage error in the measurement of volume of the black is ae BE + 2 ABI ws (1) 5% (2) 10% (3) 15% AT 4% The smallest division on main scale of a | vernier calliper is 1 mm and 10 vernier scale ye - 0.16" divisions coincide with 9 main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between 10.2 cm and 10.3 cm and the third division of vernier scale coincide with a main scale division. Find length of the wire. = 10°2 + 0-01(3) (1) 10.03 cm (2) 10.33 cm (02) (3) 10.2 cm {4} 10.23 em = 4. 45. If the least count of the scale shown is 0.1. mm, : : ‘ . iner iS 43, The vernier scale of a.calliper is divided into then the reading of the vernier calipers om 36 divisions which coincide with 29 main scale 9 | ‘2 divisions. Each main scale division is 0.3 mm.- _ im rh Aran sil citi The Jeast count of the instrument is © Sovsp = 2amsp I | . 10 (1) 0.03:mm 2) 0.01 mm * 88° = 2m a sy 9 a ° ‘4 = 24x orm ry & 0-0 (FY {3) 0.15 mm (4) 0.3 min 22x am oy 1.5 mm pee 24. Let main scale’ division be of 1 mm and SO =o" 11 ew divisions of vermier scale coincide with 49 divisions t«- "> yr ‘Tmm Wa mM of main scale. The least count of instrument is *(4) 10.7 mm {1) 0.01.mm (2) 0.1 mm 370.02.mm | (4) 0.002 mm 45. Avemier calliper has 1 mm mark on the main scale. It has 20 equal divisions on the vemier scale which match with 12 main scale divisions. Its least count is Iovsn = 45 Ms6 Vsb = 0-98 mip, " 20 vsB = 42 MSD (17.0.1 mm vse = Ea ie. (2): 0:2.mm~ a¥ - Gx0.4 mm = hae? 51. : (4)0.6 mm Le =. 1mm = Ob mm = 04mm 26... nedivisions on the main scale of a vernier calipers coincide with n + 4 divisions‘on the vernier scale. If each division on the main scale is of x units, determine. the least count of the instrument. : x APBD (nF) VSD a) = enor a n+ vso = (x x 4) 2 Oo. nti = ME What is the reading of vernier scale shown in figure? bed —+ 63 +01(4) C4 ¥ Le = ete | 46 e585 Vernier scale (1) 60.7 mm (2) 61.3 mm | (3)°62:4.mm ((4)-63,7 mm | The figure shows a situation when jaws of vemier are touching each other and one main scale divisionis of 41mm. The zero correction in measured reading = C= . will be am = o.lmm it) . -|Readliny = 9-1 (9) we : 7: = term eu 0. 5 10 Ciect (1) 0.56 mm (2) O.7MM — eerrection =-o (3) -0.5 mm U4y -0.7 mm = no +3 ape . Corporate Office : AESL, 3rd Floor, Incuspaze Campus-2, lot-13, Sector-18, Udyog Vihar, Gurnugram, Haryana-122013 pe net 4 LC Siro Palys | on & (ee hay. 2011] oO A he Hime gh! i" porn wanes tho oupth a well by omen rns a wie me Th ww dropping A stone anal muctiving the sound of imp me the ny . an bettom of well. The ewer im hi wmusswument HF Het is Stag nd do be L= 20m. Take a) a he meorus “the clepth ng woe , € the! 6. ace™® clue +o gravity a= Wms? XA the meseotia) a sound is ope Tren the fractional amnsr im tht meorvumenrt 4 St is doses tp a b) 57 ce) 3% ay oz’. Sl" — For Clrepping Str , Fer souncl +p Sach - i v= Ss | s 5 ies tote 3 20 = 1 Ug) tt 4, = 20 2 = Zoo i le = 2 sec Leu ' +, = Sok Evcr mt, : = Lb 3 ans v 920) 0 ou = tan +1 ag Ati = At + gv 7 2h P34 i L vO we t, = LALA, = At, + Atle) ar, ~ ALI 2) | At, = St A | tt. = ' | L 7 SEG) i | Given im qua: eerorin Hime | at = 0.04 sec | 5 At = At, + At, = 0-0) | AL + AL = do 5 L is -L 16 AL - go. v1 or om = “LAL = coi xig ye oO 16 [see Adv: 2016] aleoumine Hho acc” Out “tD growity q, the formu an an expoumend sto -a uae for Hme period 4 periodic molim is T = an fale be (60 +)mm 54 The values R&P are wmeosned +o naspectivel . Bn five consecutive miompuments , and (ro ae Nmm , +he A+Vme period ws jrund to be os2s , OBGE, O37 osgs . “Whe least eount of tho, Looe usect fer o ime petiod iS OOS. Which of He following ctodtment (s) is Jane rus ! woman exncr in -~ is 10% Ws SStY , OB4as, pr ™ eur in T co) The eur in TS Oey vay Te emer is 3 is wl. iM Theon = OBZ + OBL + O'BF FORA OBI ~ 5998 = 0-556 5 Ss . = O56 At, = 0567082 = 0-04 \ Le) +A At, = O56 7056 = © | AE = Jat) + \ At.) + fats) 4 (tel ay Ss At; = 056 7 a = — o64 = O62 = 004+ O + OI t DOZ TOOT At, = O86 | = = 066 — 059 = -—0-03 ‘s = O10 = 0.02 ' 5 eh AT = ef0% x10 =[s5r% J aT oe 26 = ; a = (Io + !)mm 2 eA = Lb xK!OD ~ or | Cay = pe 2 fie% | y 4 \ AT A(R-r) x 100 » 4 Gg = L yo) 2(Stxw) + (R-0) 3 es x ov R-21) 2 a 2.( 3-57) So 2 xi Lo Alaer) = Br + BR Cp ~ bebe ya = 144 4 = 114% Jw = Damen | _ 4 fungi . a swt is (25+ o-s)em , then a) Eerer BYA erouer in leapt: I" gay B= oem b) "2 erroy = 2® x 100 = 207, Ds S | 4h Q=(2stol em, Wen Which ; ia folrorsuy is fue yo = 2bem 2) = 23em 5) f= SEC 2-1em 4) R= daar. -Errer in mathemeticad operations :- ervey in ‘+! openction — let a aucctty ‘x! ale penols on anothon quanditd tar ® 'b? Vike _ oa = K(at+b) how, K =tenstont Avec = K (Aa + Ab) Now, RE = & = kK (Aa+ bby = sa = re = Aart bb (a+ b) ab Srrop_ im '—' opereedio — let ox = K(A-B) Bo = K (OA + BB) Nw, Re =XOA+S8) = AR+4B K(A-8) A-8 error iW multi ptication X% atvision Opertoctor _ a - KAT B* Cc pe? we = fs) + (88) + ° (aE) + san) K = wnsiont Ax = p/ar AX. x19 P (8 xi) + 4 (SE x0) + "(A see) + $ ( AB x0) Wxoo= pun + 48 t rhe + $%p valid upte eeter Sif. of inetiviclud) quonntiien! x Sa af gy Fed | As C.b 3d S/S loge I aay ‘oe emer iM >taolivs sh sphere is oy, “then, a) he erroy in ance by oA ervey in volume t | Set | . (ay Ares = er by *% exouse in vols = Gy Lerrm in ana = 2 (22! x00) = 4%, — 1c & 4 OLA Sh AOI pons jis (row + ON) mm? , Then “ . "ee 7 y In Side. ” Bet Mb sears ag ae =O eS fio 2 ow} 1 exovsr © Seops,, aan 5 D) A enrter IW cola = BA y i507 Leo ‘ 4 + A= (loo + ot) € | ®& B = (oo +o0-2) then, ea a) 2(A+e) b) 2(a-B) ae ok | i} Ax = 2(01 +02) dbx = 2(o1 +02) be caves o 7 Tey te ele = O-& = OG | | Axe OF | Reodiny = 40 +06 Reading = (04 0 a) TOs ne com al \ wes Ax =0+03 Rtaaiy = (100 + 3) ae chee a hq =? war = 4%, 7 ; Res = on * Sel hy = + DAT in , 7 og = 27 %oT = bq x 3 d a 1G . vet a a = LP +4277 | = 2 4 24) = J0%7. a he @ afl pow 4 ae 21 Ga pe ax [Et ews _ = ) "vate 
