Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed and magnitude f maximum transverse acceleratin f a pint n the string are 4. m/s and 840 m/s, respectively. What is the speed f waves n the string? A) 48 m/s B) 17 m/s C) m/s D) 66 m/s E) 53 m/s v = λf but λ = L = 0.75 = 1.5 m f = ω π = 1 π a max = 84.0 u max 4. 1 = 31.83 Hz π v = λf = 1.5 31.83 = 47.8 m/s Q. A sund wave is travelling in air. The intensity and frequency f the wave are bth dubled. What is the rati f the new pressure amplitude t the initial pressure amplitude? A) B) 1/ C) 1 D) E) 1/ P max = Iρv = Iρλf but v = λ 1 f 1 = λ f ; f = f 1 then λ = λ 1 P 1 max = I 1 ρλ 1 f 1 f 1 P max = I ρλ 1 = I 1ρλ 1 f 1 = 4I 1 ρλ 1 f 1 P max = 4I 1ρλ 1 f 1 P 1 max I 1 λ 1 f 1 = P max P 1 max = c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: Q3. A cpper cntainer with a mass f 0.500 kg cntains 0.180 kg f water, and bth are at a temperature f 0.0 C. A 0.50 kg blck f irn at 85.0 C is drpped int the cntainer. Find the final equilibrium temperature f the system, assuming n heat lss r gain t the surrundings. [specific heat (J/kg.K): cpper = 390, irn = 470] Q + = Q A) 7. C B) 33.1 C C) 5.5 C D) 13.7 C E) 95.3 C (m cu c cu + m water c water ) T f 0 = m irn c irn 85 T f T f = 85 m irn c irn + (m cu c cu + m water c water ) 0 m cu c cu + m water c water + m irn c irn T f = 85 0.5 470 + (0.5 390 + 0.18 4190) 0 0.5 390 + 0.18 4190 + 0.5 470 = 7.16 = 7. Q4. An ideal diatmic gas is initially at 7 C and a pressure f 1.0 atm. It is cmpressed adiabatically t ne fifth f its initial vlume. What is the final pressure (in atm) f the gas? A) 9.5 B).5 C) 5. 0 D).9 E) 15 P i V γ i = P f V γ f P f = P i V γ i = 1 51 1.4 V = 9.5 atm f c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 3 Q5. A blck f ice f mass 1.00 kg at 0 C is heated until it becmes water at 100 C. Calculate the entrpy change f the ice until it becmes water at 100 C. A).53 kj/k B) 1.57 kj/k C) 1. kj/k D).31 kj/k E) 1.47 kj/k S = m ice L f 73 1 333 103 = 73 S =.53 10 3 J/K + m water c water ln 373 73 + 1 4190 l n 373 = 59.4 J/K 73 Q6. Three pint charges are arranged as shwn in FIGURE 1. Charges Q 1 and Q 3 are psitive, charge Q is negative, and the magnitudes f Q 1 and Q are equal. What is the directin f the net electrstatic frce n Q 3 due t Q 1 and Q? A) Negative y directin B) Psitive y directin C) Psitive x directin D) Negative x directin E) The net frce n Q3 is zer Figure 1 A c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 4 Q7. Tw pint charges,.50 µc and 3.50 µc, are placed n the x axis, as shwn in FIGURE, ne at the rigin and the ther at x = 0.600 m, respectively. Find the crdinate f a pint n the x axis where the electric field due t these tw charges is zer. A) 3.7 m B) + 3.7 m C) + 0.80 m D) + 0.880 m E) 0.880 m E 1 P F Figure At P E 1 = E d kq 1 d = kq (0.6 + d) q 1 = d 0.6 + d d q 0.6 + d = q 0.6 + d d q 1 = 3.5.5 = 1.18 = 1.18 (1.18 1)d = 0.6 d = 0.6 = 3.7 m = 3.7 m 0.18 c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 5 Q8. A small sphere with a mass f 4.00 10-6 kg and carrying a charge f 50.0 nc hangs frm a string near a very large, charged insulating sheet, as shwn in FIGURE 3. The charge density n the surface f the sheet is.50 nc/m. What is the angle (θ) which the string makes with the vertical? A) 10. B) 19.8 C) 70. D) 79.8 E) 45. Tsinθ = qe Tcsθ = mg Tsinθ Figure 3 Tcsθ Tsinθ T qe Tanθ = qe σ q mg = ε 0 mg q σ θ = tan 1 ε 0 mg = 50 10 9.50 10 9 tan 1 4 10 6 9.8 8.85 10 1 = 10. mg c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 6 Q9. Tw pint charges, carrying equal magnitude f charge, are arranged in three cnfiguratins as shwn in FIGURE 4. Rank the cnfiguratins accrding t the wrk dne by an external agent t separate the charges t infinity, greatest first. A) 1,, 3 B) 3, 1, C) 3,, 1 D) 1, 3, E), 3, 1 W ext = U i = kq 1q d Figure 4 W 1 ext = + kq d ; W ext = + kq d ; W 3 ext = kq d Q10. The electric ptential at pints in a xy plane is given by V = 1.5 x 3.5 y (where V is in vlts and x and y are in meters). In unit-vectr ntatin, what is the electric field (in V/m) at the pint (.0, 3.0) m? A) 6.0iˆ+ 1 ˆj B) + 6.0iˆ 1 ˆj C) 6.0iˆ 1 ˆj D) + 6.0iˆ+ 1 ˆj E) 1iˆ+ 6.0 ˆj E (,3) = E x ı + E y ȷ E x = V x = 3x; E y = V y = +7y E x (x = ) = 6 ; E y (y = 3) = +1 E = E x ı + E y ȷ = 6ı + 1ȷ c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 7 Q11. In FIGURE 5, ptential difference acrss 5.0 µf capacitr is V ab = 8 V. What is the charge n the 11 µf capacitr? A) 77 µc B) 140 µc C) 63 µc D) 54 µc E) 86 µc q 5μF = C 5μF V = 5 10 6 8 = 140μF C 9 11 = C 9μF + C 11μF = (9 + 11)μF = 0μF Figure 5 V 11 = q 5μF C 9 11 = 140 10 6 = 7V 0 10 6 q 11 = C 11 V 11 = 11 10 6 7 = 77μC Q1. What is the magnitude f the electric field in a cpper wire, f radius 1.0 mm, that is needed t cause a.75 A current t flw? Cpper has a resistivity f 1.7 10-8 Ω.m. A) 0.0145 V/m B) 0.317 V/m C) 0.0464 V/m D) 0.0547 V/m E) 0.108 V/m R l = ρ A ; E = V l = ir l = i ρ i ρ = A πr =.75 1.7 10 8 π (1.00 10 3 = 0.0145 V/m ) c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 8 Q13. Find the current thrugh 4.00 Ω resistr in the circuit, shwn in FIGURE 6 (Nte that the emfs are ideal). Figure 6 A) 1.11 A B) 5.1 A C) 6.3 A D) 0.75 A E).67 A 0 i 1 14 + 4i 3 = 0 i 1 = 3 + i 3 (1) 36 5i 4i 3 = 0 5i = 36 4i 3 i = 7. 0.8i 3 () i = i 1 + i 3 i 1 i Frm () 7. 0.8i 3 = i = i 1 + i 3 7. 0.8i 3 = 3 + i 3 + i 3 = 3 + 3i 3 3i + 0.8i 3 = 7. 3 = 4. i 3 = 4. = 1.11 A 3.8 Q14. Five resistrs are cnnected as shwn in FIGURE 7. What is the ptential difference V A V B, if the current thrugh the.70 Ω resistr is 1. A? A) 15.0 V B) 19.0 V C) 10.7 V D). V E) 5.54 V V A V B = (i 1 + 1.)R eq.7 1. i 1 = = 0.51 A 6.5.70 6.50 R eq = 3.0 + + 3.60 = 8.71 Ω.70 + 6.50 V A V B = (i 1 + 1.)R eq = (0.51 + 1.) 8.71 = 15.0 V i 1 Figure 7 1. A c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 9 Q15. In FIGURE 8, fur identical resistrs are cnnected t an ideal battery. S 1 and S are switches. Which f the fllwing actins wuld result in the minimum pwer dissipated in resistr A? Figure 8 P min = A) keeping bth switches pen B) clsing S 1 nly C) clsing bth switches D) clsing S nly E) The answer depends n the value f the emf f the battery V R max R max fr bth swithces pen nly! R max = R + R = R Q16. V = ε ir Each f the tw real batteries in FIGURE 9 has an emf f 0.0 V and an internal resistance r = 0.500 Ω. What is the ptential difference acrss each battery if R= 5.00 Ω and the current in resistr R is 3.80 A? A) 19.1 V B) 10.1 V C) 5.50 V D) 9.55 V E) 0.0 V 1.9 A 1.9 A Figure 9 = 0 1.9 0.5 = 0 0.95 = 19.05 = 19.1 V i = 3.8 A c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 10 Q17. A 00 µf capacitr, that is initially uncharged is cnnected in series with a 6.00 Ω k resistr and an emf surce with ε = 00 V and negligible resistance. The circuit is clsed at t = 0. What is the rate at which electrical energy is being dissipated in the resistr at t = 1.00 s? A) 1.6 W B). W C) 0.500 W D) 3.4 W E) 5.11 W P = i (t) R ; i(t) = ε R e t/rc i(t = 1s) = 00 6000 e 1/ 6000 00 10 6 = 1 30 e( 1/1.) = 1 30 e 0.833 = 0.0145 A 30 P = i (t) R = (0.0145) 6000 = 1.6 W Q18. An electrn has a velcity f 6.0 10 6 m/s in the psitive x directin at a pint where the magnetic field has the cmpnents B x = 3.0 T, B y = 1.5 T, and B z =.0 T. What is the magnitude f the acceleratin f the electrn at this pint? (Ignre gravity) A).6 10 18 m/s B) 1.6 10 18 m/s C).1 10 18 m/s D) 3. 10 18 m/s E) 3.7 10 18 m/s a = F B = q e(v B) = 1.6 10 6.0 19 106 ı 3ı + 1.5ȷ + k m e m e 9.1 10 31 = 1.6 10 19 6 10 6 9.1 10 31 1.5(ı ȷ ) + ı k = 1.05 10 18 1.5k ȷ a = 1.05 10 18 6.5 =.6 10 18 m/s c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 11 Q19. In FIGURE 10, current i = 50.0 ma is set up in a lp having tw radial lengths and tw semicircles f radii a =10.0 cm and b =0.0 cm with a cmmn center P. What is the magnitude f the lp s magnetic diple mment? μ = NiA A) 3.93 10-3 A.m B) 1.16 10 A.m C) 5.11 10 A.m D) 4. 10 A.m E).3 10 A.m μ = iπ (r a + r b ) = 50 10 3 π (0.1 + 0. ) = 3.93 10 3 A m Figure 10 Q0. A particle (m = 3.3 10 7 kg, q = 1.6 10 19 C) is accelerated frm rest thrugh a 10 kv ptential difference and then mves perpendicular t a unifrm magnetic field with magnitude B = 1. T. What is the radius f the resulting circular path? A) 17 mm B) 19 mm C) 0 mm D) 10 mm E) 9.0 mm F B = qvb = F R = mv R mv R = qb but qv = 1 mv v = qv m R = mv qb = m qb qv m = 1 B mv q = 1 1. 3.3 10 7 10000 1.6 10 19 R = 0.017 m = 17 mm c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A 5.0 A current is flwing in a 5.0 m lng wire which is aligned alng the directin f the unit vectr 0.60 î + 0.80 ĵ. The wire is placed in a regin where the magnetic field is given by B = 0.80 kˆ (T). The magnitude f the magnetic frce n the wire is: F B l A) 0 N B) 3 N C) 59 N D) 17 N E) 40 N = i l B F B = li l B = 5 5 (0.6ı + 0.8ȷ ) 0.8k F B = 5 0.6 0.8 ı k + 0.8 0.8 ȷ k = 5 0.48( ȷ ) + 0.64(ı ) = 5 0.64 ı 5 0.48 ȷ = 16ı 1ȷ F B = 16 + 1 = 0 N Q. An electrn mving with a velcity v = 5.0 10 7 m/s î enters a regin f space where perpendicular electric and magnetic fields are present. The electric field is E = 1.0 10 4 ĵ. What magnetic field will allw the electrn t pass thrugh the regin, undeflected? A A) B = ( ) B) B =+ ( ) C) B = ( ) D) B =+ ( ) E) B =+ ( ).0 10 T k 4 ˆ.0 10 T j 4 ˆ.0 10 T i 4 ˆ.0 10 T k 4 ˆ 5.0 10 T k 4 ˆ c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 13 Q3. The lp shwn in FIGURE 11 cnsists f tw semicircles 1 and (with the same center) and tw radial lengths. The semicircle 1 lies in the xy plane and has a radius f 10.0 cm, and the semicircle lies in the xz plane and has a radius f 4.00 cm. If the current i in the lp is 0.500 A, what is magnitude f the magnetic field at pint P, lcated at the center f the lps? Figure 11 A) 4.3 µt B) 3.71 µt C) 1.37 µt D).9 µt E) 6.45 µt B net = B ȷ + B 1 k B 1 = μ 0i = 4π 10 7 0.5 = 15.71 10 7 T 4R 1 4 0.1 B = μ 0i = 4π 10 7 0.5 = 39.7 10 7 T 4R 1 4 0.04 B net = B 1 + B = (15.71) + (39.7) 10 7 T = 4.3μT c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 14 Q4. FIGURE 1 shws three lng, parallel, current-carrying wires carrying equal magnitude f current. The directins f currents I 1 and I 3 are ut f page. The arrw labeled F represents the magnetic frce per unit length acting n current I 3 due t the ther tw wires and is given by F = ( 0.0 î 0.0 ĵ ) (N/m). What are the magnitude and directin f the current I, if the distance d = 1.00 mm? Figure 1 A) 33. A, int the page B) 33. A, ut f the page C).1 A, int the page D).1A, ut f the page E) 11.4 A, ut f the page F = 0.ı 0.ȷ = F 13 ı F 3 ȷ F 3 = 0. = μ 0i 4π 10 7 = i πd π d 0. d i = 10 7 = 0. 10 3 10 7 = 33. A int the page c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 15 Q5. Tw infinitely lng current-carrying wires are parallel t each ther, as shwn in FIGURE 13. The magnetic field at pint P, which is midway between them, is 0.1 mt ut f the page. If the current I 1 = 1 A, what is magnitude and directin f I? A) 1 A, t the right B) 1 A, t the left C) 3.0 A, t the right D) 3.0 A, t the left E) 15 A, t the left B net = 0.1 10 3 T = B 1 + B Figure 13 B = 0.1 10 3 B 1 B 1 = μ 0i 1 πd = 4π 10 7 1 = 16 10 5 T π 0.015 B = 0.1 10 3 + 0.16 10 3 = 0.8 10 3 B 1 = μ 0i πd i = πdb μ 0 = πdb 4π 10 7 i = db 0.015 0.8 10 3 = 10 7 10 7 = 1A Q6. Which f the slenids described belw has the greatest magnetic field alng its axis? A A) a slenid f length L, with N turns and a current I B) a slenid f length L, with N turns and a current I C) a slenid f length L, with N/ turns and a current I D) a slenid f length L/, with N/ turns and a current I E) a slenid f length L, with N turns and a current I/ c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 16 Q7. A cylindrical cnductr f radius R =.50 cm carries a.50 A current alng its length. This current is unifrmly distributed thrughut the crss sectinal area f the cnductr. Find the distances frm the center f the wire (inside and utside the wire) at which the value f magnitude f magnetic field equals half f its maximum value. B ut = A) 1.5 cm, 5.00 cm B) 1.50 cm, 6.50 cm C) 1.00 cm, 4.00 cm D) 1.5 cm, 7.50 cm E) 1.50 cm, 3.00 cm μ 0i = 1 πr cm μ 0i πr = 1 B max 1 = R cm 1 R R ut = R =.50 = 5.0 cm B in = μ 0i πr R r = B max = 1 μ 0i πr r R = 1 r = R =.50 = 1.5 cm B in at r = 1.5 cm, B ut at r = 5.00 cm Q8. A 0-turn circular cil f radius 5.00 cm is placed in a magnetic field perpendicular t the plane f the cil. The magnitude f the magnetic field varies with time as B(t) = 0.0100 t + 0.0400 t, where B is in Tesla and t is in secnd. Calculate the magnitude f the induced emf in the cil at t = 5.00 s. db dt A) 64.4 mv B) 40.4 mv C) 3. mv D) 3.5 mv E) 30.5 mv = 0.01 + 0.08t; db dt (t = 5s) = 0.01 + 0.4 = 0.41 ε = N db dt A = 0 0.41 π(0.05) = 0.0644 V ε = 64.4 mv c-0-n-30-s-0-e-1-fg-1-f-0
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 17 Q9. A cnducting bar f length L mves t the right n tw frictinless rails, as shwn in FIGURE 14. A unifrm magnetic field, directed int the page, has a magnitude f 0.5 T. Assume R = 10 Ω, L = 0.45 m. At what cnstant speed shuld the bar mve t prduce a 9.0 ma current in the resistr? A) 0.80 m/s B) 0.85 m/s C) 0.75 m/s D) 0.70 m/s E) 0.65 m/s Figure 14 ε = BLv = ir v = ir BL = 9 10 3 10 = 0.8 m/s 0.5 0.45 Q30. Tw rectangular lps f wire lie in the same plane as shwn in FIGURE 15. If the current I in the uter lp is cunterclckwise and increases with time, which f the fllwing statements is CORRECT abut the current induced in the inner lp? A A) It is clckwise. B) It is cunterclckwise. C) It is zer. D) Its directin depends n the dimensins f the lp. E) Its directin is fluctuating with time. Figure 15 c-0-n-30-s-0-e-1-fg-1-f-0