Bphe-104 Phe-4

Tutor Marked Assignment MATHEMATICAL METHODS IN PHYSICS-I Course Code: BPHE-104/PHE-04 Assignment Code: BPHE-104/PHE-04/TMA/2019 Max, Marks: 100 Note: Attempt all questions, Symbols have their usual meanings. The marks for each question are indicated against it. 1. a) Calculate the area of a triangle whose vertices are given by (3, -1, 2), (1, -1, 2) and. (4,2, D. 6) b) Show that for any three vectors i,b and é ax (b<é)+bx(€xa)+€x(axb)=0 (6) 2. a) Determine the unit tangent vector to the following curve at t=1 i+ (CE -4N]}+ 61-0 yk 6) b) The height of a hill is defined by the scalar field A(x, y) =10(2xy-3x7 +4y? -18x+28y +12). Calculate the height of the hill at the point (1,1) and the direction of the steepest ascent at that point (5) 3. Show that for two scalar fields and g: Vir ve)|-o. 19) 4, a) Obtain the curl of the following vector A=G, +7? cosy +rsin ey) (5) b) Express the vector field F = xyzi + (x? + y)} +k in cylindrical coordinates and calculate its divergence. G) 5. Calculate the work done by a force F = (xz— y)j+2zk in moving a particle along the curve x= 27; y=1;2 = 417 -1 from 1=0 to £=1. Is the force conservatir (10) 6, Using Gauss’ Theorem caleulate the flux of the vector field F =.d + yj+ 2k through the surface of a cylinder of radius 4 and height H7, which has its axis along the 2-axis and the base of the eylinder is on the xy-plane. (10) 7. a) Show that 9-("#}=(n+3)r” 6) b) Using Green’s Theorem evaluate the integral fc? yd —xy?dy) where Cis the circle x? + y? =4 oriented counter clockwise. (3)8. A solid in the shape of a hemisphere with a radius of 2 units, has its base in the xy-plane and the centre of the base at the origin. Ifthe density of the solid is given by the function (xyz) = 292, determine the mass of the hemisphere. (10) 9, a) The probability that a patient recovers from a rare disease is 0.6. Calculate the probability that out of 5 patients suffering from this disease, at least two would recover. ) 'b) A typical sheet of metal has on the average 2 defects per 5 m’. What is the probability that a 10 m? sheet of metal will have at least 3 defects? 3) 10, The modulus of rigidity of a wire is N wr ‘The following measurements are made for Lr and 0 / N 5 0,05 mm 300 +2 mm 5.00 £0.20 ad Nn Obtain the best value of n, (10)yeotro~ pS Yedlox exons Bude (omen of pvr as, a 2), e4,-*4) | Fe qayte Cite @ rR iets» rs ees a 6 = (he%e)? y + Ubo-40)? + Cagetn) & 37+ a av pC-UF fr # sa! “ iBee ee Vector thie Perdt artert) - G-OE- VE URHD, Yad) Peale Bn Cexe) eV ree) + 2 x (& xt) ~ foxes ene leat OS rere ~ (BETe - (E R\y+& exe - (SHE ¥Ce. We - (ee ay Ctreved) mak 2.@ Unite Deuesine of ceedan, in Hw - 2d PCa Fs 4-4) F denget ted ts i) = Wa 4th + GPaaji+ (s-24)k=\0 (48-2) cor 2 = abe ef Hew ob OD 4 at ecpevt agent of _ ee pectin of de [ve ape direc 4 f hong word Fait | aca 5 kts +040) = 10 (26 -6e9 Peo, Gls ™ a1) so yo(anteo4 By 40432 0 yee aowriey 43828 = ae oa o> €220)1 Ce . oe qesseF ~ joel je 2°)" 4589): wat ‘ ees j > Lie Sx (PR) - ECAP) - ~ B, Me ® A + pean o) : : erin cost} apme) a aad Pang eos 4 r> pangeet \ ee 4) +228 ass =f aF=3(2F) rte Herve - DY Pages | Fine 3(4 44) A gah mat z #43 4424) © aie aia (ett-2e af + tt 2b) F = 5 wn a DI O44,2) = WIG hs te “ 4 iD - ex r+ ut+ Ate H)* a FIC) -Gat+Oi+ (34 -Nk ; we k pe é 4 Gstiegst gt + APF let 24)Sr > yaa. tO. gO He foree 15 wot conservative. 2 Spi) oe 6 ee ee er ces. rn eee (\G pe a Lee So “he one word Anau des, 4 So, one 2, 0-4 EF, nerpeetively. ae Ss, n= & Pdrdh ey ? SS, ~ =a The namge of he cylinder PB) BP chr 06 8 sane of ts Kod y=? cr’ c= whey ee ye enrd pek yore UmTb noaedds Se eef Pane. a(ounieea) S$ Se ih inte! 2] ee ‘S = ff & zrircq o |) zearse Sy Se 4 Fdtagee and We Kuo = i aes [eiad Se= an" bn ‘21 Ye Lae (A= Tig yt 4 na wget > = > 3 Diy Sin Va wey 3.0 9 Bere = zy +040 Seats & KA ox 2% OW. 22> SE eae paoneAS A eg © by @,0,@ we oe. 23M byt + gun” “2. ea N-2 awn + gta” - ae io tye etos Ley a wey ig 2 iS mele) bp. 6 Be ca eg* oer = |) “Aaa aa I a fos: Aner of gre cinese of nadivg Q a aH mek 2 2 4M = 4 [\ dey = cA) 5IR 2 WAR corsOarpeorp we 2 dideddg Oia) \ H? dt Bm Des dO Amd wrdd 9° ge?920 2 Fe [yf] ayPocerode ringerradd ie Sr x gO ow at C4 ) jo" pcoro dh amd cong ad Be. e. Bae ot 64 ae te te] Steerer 6 oe 7" cain a ° he a ibe:rihy of 3 necoun- abl 5, 0-6) oe — 3 Ke raae Wie : ao eras — PPprelebrnty oF Arie coven. Bint ty, o +6) me. x eu ea am i Ayr)! 2 0-259 5 fro looks lity oh chs neces eb ls oe) l a, 5 Soo oe , ce) 40-24) { i 6) A?) 44%6 oktestee gehee i LO wm = 2x0 = 4DY PY nk Ue mean Ueliea * 97 > (9)

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