PHY2054 Exam 1 Formula Sheet

Transcription

1 Instucto: Pofs. Fiel, Kotov PHYSICS DPARTMNT PHY 54 Final xam Decembe, 5 Name (PRINT, last, fist): Signatue: On m hono, I have neithe given noeceive unauthoize ai on this examination. YOUR TST NUMR IS TH 5-DIGIT NUMR AT TH TOP OF ACH PAG. DIRCTIONS () Coe ou test numbe on ou answe sheet (use 76 8 fo the 5-igit numbe). Coe ou name on ou answe sheet. DARKN CIRCS COMPTY. Coe ou stuent numbe on ou answe sheet. () Pint ou name on this sheet an sign it also. (3) Do all scatch wok anwhee on this exam that ou like. At the en of the test, this exam pintout is to be tune in. No ceit will be given without both answe sheet an pintout with scatch wok most uestions eman. (4) lacken the cicle of ou intene answe completel, using a # pencil o blue o black ink. Do not make an sta maks o the answe sheet ma not ea popel. (5) The answes ae oune off. Choose the closest to exact. Thee is no penalt fo guessing. >>>>>>>>WHN YOU FINISH <<<<<<<< Han in the answe sheet sepaatel. Constants ǫ = 8.85 F/m m e = 9. 3 kg m p = m n =.67 7 kg e =.6 9 C k = N m /C µ =.56 7 H/m N A = 6. 3 atoms/mole c = 3 8 m/s milli = 3 mico = 6 nano = 9 pico =

2 PHY54 xam Fomula Sheet ectos a = a xˆ x + a ˆ + azzˆ b = bxxˆ + b ˆ + bz zˆ Magnitues: a = ax + a + az b = bx + b + bz Scala Pouct: a b = a b + a b + a b = a b cosθ (θ = angle between a an b ) lectostatic Foce (vecto): lectic Fiel (at ue to ): x x z z lectostatic Foce an lectic Fiel F = k ˆ ( = istance between chage an chage, units = N) k = /(4πε ) = 8.99x 9 N m /C ε = 8.85x - C /(N m ) = F / = k ˆ (units = N/C = /m) Φ = A lectic Flux (though the infinitesimal suface aea A): (units = Nm /C) ecto Aea (iecte aea): A= Anˆ (whee nˆ = nomal to the suface) Gauss aw (net flux though close suface S): Φ = S A= enclose ε ( enclose = chage enclose) Gauss aw: Net flux though close suface S = the chage enclose b suface S ivie b ε lectic Potential an Potential neg lectic Potential neg: wok one against a constant fiel in moving chage a istance along staight line path fom A to, U = U U A = (units = J) lectic Potential: Wok one pe unit chage against a constant fiel in moving chage a istance along staight line path fom A to, lectic Potential (istance fom a point chage ): lectic Potential neg (N point chages): = U / = (units = J/C = ) U = N i ( ) = k N point chages: ( ) = k Stoe lectic Potential neg (N conuctos with chage i an electic potential i ): N i= i i Capacitance (efinition): C = / o C = / (units = C/ = F) neg Densit of the lectic Fiel: u= ε (units = J/m 3 ) Cuent (though iecte aea A): lectic Cuent an Cicuits I = J A= nvift A t, i= N U = i= = (units = C/s = A, n is the numbe of chage paticles pe unit volume, v ift is the aveage velocit of the chage paticles). Conucting Wie (length, coss sectional aea A): Ohm s aw: = IR, R ρ / A = (Resistance R units = /A = Ω) J = σ, I = σ A= A/ ρ, = Resistivit (at tempeatue T in o C): ρ ( T ) = ρ(+ α T ), whee T = T T Powe (supplie b MF ε): P = εi Powe (issipate in esisto R): P = I R (units = J/s = W) t /τ RC Cicuits (chaging capacito C though esisto R with MF ε): ( t) = εc( e ) RC Cicuits (ischaging capacito C with initial chage though esisto R): RC Cicuits (time constant):τ = RC (units = Ω F = s) whee i is the electic potential at i ue to the othe chages ( t) = e t /τ i i i

3 PHY54 xam Fomula Sheet ectos a = a xˆ x + a ˆ + azzˆ b = bxxˆ + b ˆ + bz zˆ Coss Pouct Magbitue: a b = a b sinθ Coss Pouct ecto: c = a b = ( a b a b ) xˆ ( a b a b ) ˆ + ( a b a b ) zˆ F z z x z z x lectomagnetic Foce = F + F = + v F = F = v lectmagnetic Foce (vecto): M ( = istance between chage an chage, v = velocit of chage, = velocit of chage ) F = k ˆ (units = N) F = k v c x ˆ x (units = N) k = /(4πε ) 8.99x 9 N m /C ε 8.85x - C /(N m ) k = k/c =µ /(4π) -7 Tm/A µ 4π -7 Tm/A c 3 8 m/s (spee of light) lectic Fiel (ue to ): Magnetic Fiel (ue to ): Magnetic Fiel (ue to cuent I): neg Densit (lectic & Magnetic Fiel): = k ˆ (units = N/C = /m) = k ˆ (units = N/(C m/s) = T) I = k l ˆ (units = N/(C m/s) = T) u = ε u = (units = J/m 3 ) µ F = I (units = N) µ = NIA (units = A m ) A= Anˆ τ =µ (units = N m) Magnetic Foce (on a long staight wie caing cuent I): Magnetic Dipole Moment (N loops, cuent I, aea A): Magnetic Toue on a Magnetic Dipole: Ampee s aw: l = l= µ C C Infinite Staight Wie Caing Cuent I: I enclose Cente of a Cicula oop Caing Cuent I: (aoun a close loop) Magnetic Fiel (xamples) = ki / pep = π k I / R = µ ni Infinite Solenoi (cuent I, n loops pe unit length): (units = T) (units = T) (units = T) lectomagnetic Inuction, R Cicuits, an C Cicuits Φ = A= Acosθ A Magnetic Flux (unifom, suface A): = Φ Faaa s aw of Inuction: ε = (ε = inuce MF, units = ) t I Inucto (inuctance units = H): = (potential iffeence) U = I t R Cicuits (time constant):τ = /R (units = H/Ω = s) t R Cicuits (MF ε, Resisto R, Inucto, swich close at t = ): I( t) = ε ( e Oscillating C Cicuit (no esistance): U / C I tot + pep units = Tm = Wb /τ ab (stoe eneg) ) / R = (stoe eneg) ω= / C Oscillating C Cicuit (no esistance): ( t) = sin( ω t+ ϕ) I( t) = I cos( ω t+ ϕ) Oscillating C Cicuit (no esistance): f = ω/π (feuenc of oscillations in Hz)

4 Rick s ectues: Close Cuve PHY54 Final xam Fomula Sheet Ampee s aw (complete) Φ l = µ Ienclose + µ ε Textbook: l= µ Ienclose + µ ε t ( x, t) = ( x, t) = max max Close Cuve lectomagnetic Plane Wave sin( kx ωt) ˆ sin( kx ωt) zˆ ( x, t) = c( x, t) ω c Spee in acuum: c= = fλ = Spee in Meium (n = inex of efaction): v n = < c k µ ε n λ Wavelength in Meium: λ n = n Ponting ecto: S =, µ Intensit: (λ = Wavelength in acuum, n = inex of efaction) P S = S = = = µ µ c A powe P powe ms cms c I = S = = = = = (units = W/m ) A µ c µ µ c µ (units = W/m ) Intensit Tansmitte b a Poloize: I = I (anom) I = I cos θ (polaize) Relativistic Dopple Shift (f = feuenc at est with souce, λ = wavelength at est with souce, fλ = c) + β β λ awa = λ f awa = f β = / c β + β Souce Moving Awa fom Obseve: Souce Moving Towa the Obseve: Snell s aw: λ towa = β + β = λ f towa = f β / c + β β Φ t ( = elative velocit) ( = elative velocit) Reflection & Refaction n sinθ = n sinθ Total Intenal Reflection in Meium (): sin = n / n c tanθ = n n ewste s Angle in Meium (): Mios & Thin ens Spheical Mios (R = aius of cuvatue): f = R / Object an Image Position (mios & thin lens): = + f p Magnification (mios & thin lens): m=, h = m h p Reflection in Meium : (phase shift n > n ) Maximal Constuctive: (phase shift) Maximal Destuctive: (phase shift) ) / θ (n < n ) Reflection & Intefeence φ = π (phase shift n < n ) φ = φ = πm (lateal shift) l= mλ m=, ±, ±, φ = π ( m+ (lateal shift) l= ( m+ ) λ m=, ±, ±, Wavelength (in m): λ Wavenumbe (in m - ): k = π/λ Angula Feuence (in a/s): ω = πf Feuenc (in Hz): f Peio (in s): T = /f f = focal length (> concave, < convex) p = objct istance = image istance (> eal, < vitual) h = object height h' = image height m = magnification (> upight, < invete) Intensit: (max constuctive) I = I+ I+ II (max estuctive) I = I+ I II Single-Slit Minima: sinθ = mλ Resolving Powe (lens iamete D: θ.λ / D Double-Slit (an gating): (max constuctive) sin θ = mλ (max estuctive) sinθ = ( m+ ) λ

5 . Consie a cube of sies = m as shown in the figue an suppose that a non-unifom electic fiel is pesent an is given b (x) = (a bx)ˆx, whee a = an b = /m ae constants. What is the net electic chage (in nc) containe within the cube? O -axis z-axis () 7.8 () 3.9 (3) (4) +7.8 (5) Consie a cube of sies = 3 m as shown in the figue an suppose that a non-unifom electic fiel is pesent an is given b (x) = (a bx)ˆx, whee a = an b = /m ae constants. What is the net electic chage (in nanoc) containe within the cube? O -axis z-axis () 3.9 () 7.8 (3) (4) +7.8 (5) Consie a cube of sies = 4 m as shown in the figue an suppose that a non-unifom electic fiel is pesent an is given b (x) = (a bx)ˆx, whee a = an b = /m ae constants. What is the net electic chage (in nanoc) containe within the cube? O -axis z-axis () () 7.8 (3) 3.9 (4) +7.8 (5) A soli insulating ball with aius R has a unifom chage ensit ρ an total chage +. Thee is a point chage = + embee at the cente of the insulato (not pat of the insulato). The insulating ball is suoune b a spheical conucting shell with inneaius R an outeaius 3R/ as shown in the figue. The net chage on the conucto is +. How much chage is locate on the oute suface ( = 3R/) of the conucto? Point chage at oigin () +4 () +5 (3) +6 (4) zeo (5) Insulato net chage = + 3R/ R Net chage + on conucto 5. A soli insulating ball with aius R has a unifom chage ensit ρ an total chage +. Thee is a point chage = +3 embee at the cente of the insulato (not pat of the insulato). The insulating ball is suoune b a spheical conucting shell with inneaius R an outeaius 3R/ as shown in the figue. The net chage on the conucto is +. How much chage is locate on the oute suface ( = 3R/) of the conucto? Point chage at oigin () +5 () +4 (3) +6 (4) zeo (5) Insulato net chage = + 3R/ R Net chage + on conucto

6 6. A soli insulating ball with aius R has a unifom chage ensit ρ an total chage +. Thee is a point chage = +4 embee at the cente of the insulato (not pat of the insulato). The insulating ball is suoune b a spheical conucting shell with inneaius R an outeaius 3R/ as shown in the figue. The net chage on the conucto is +. How much chage is locate on the oute suface ( = 3R/) of the conucto? Point chage at oigin () +6 () +4 (3) +5 (4) zeo (5) Insulato net chage = + 3R/ R Net chage + on conucto 7. A chage paticle taveling to the ight along the negative as shown in the figue has an initial kinetic eneg of 8µJ. At x = it expeiences a non-unifom electic potential given b (x) = bx 3, whee b = 5 /m 3 is a constant an x is measue in metes. If = µc, what is the lagest positive x-value (in metes) eache b the paticle befoe it comes to est? () () 3 (3) 4 (4) (5) 5 -axis 8. A chage paticle taveling to the ight along the negative as shown in the figue has an initial kinetic eneg of 7µJ. At x = it expeiences a non-unifom electic potential given b (x) = bx 3, whee b = 5 /m 3 is a constant an x is measue in metes. If = µc, what is the lagest positive x-value (in metes) eache b the paticle befoe it comes to est? () 3 () (3) 4 (4) (5) 5 -axis 9. A chage paticle taveling to the ight along the negative as shown in the figue has an initial kinetic eneg of 64µJ. At x = it expeiences a non-unifom electic potential given b (x) = bx 3, whee b = 5 /m 3 is a constant an x is measue in metes. If = µc, what is the lagest positive x-value (in metes) eache b the paticle befoe it comes to est? () 4 () (3) 3 (4) (5) 5 -axis. Thee point chages =, =, an 3 = ae fixe at the vetices of an euilateal tiangle with sies of length as shown in the figue. If =, how much wok is euie to move chage to the mi-point of the staight line between an 3? Note k = /(4πǫ ). () 4k / () 6k / (3) 8k / (4) k / (5) k /. Thee point chages =, =, an 3 = ae fixe at the vetices of an euilateal tiangle with sies of length as shown in the figue. If = 3, how much wok is euie to move chage to the mi-point of the staight line between an 3? Note k = /(4πǫ ). () 6k / () 4k / (3) 8k / (4) k / (5) k /

7 . Thee point chages =, =, an 3 = ae fixe at the vetices of an euilateal tiangle with sies of length as shown in the figue. If = 4, how much wok is euie to move chage to the mi-point of the staight line between an 3? Note k = /(4πǫ ). () 8k / () 4k / (3) 6k / (4) k / (5) k / 3. A positivel chage paticle with a chage to mass atio /m = C/kg is taveling to the ight along the with spee = m/s. At t = an x = it encountes unifom anti-paallel electic an magnetic fiels. The magnetic fiel points in the positive x-iection an the electic fiel points in the negative x-iection, as shown in the figue. If the magnitues of the an fiels ae. /m an. T, espectivel, what is the paticle s spee (in m/s) at t = s? () () (3) (4) 3 (5) 4 -axis 4. A positivel chage paticle with a chage to mass atio /m = C/kg is taveling to the ight along the with spee = 3 m/s. At t = an x = it encountes unifom anti-paallel electic an magnetic fiels. The magnetic fiel points in the positive x-iection an the electic fiel points in the negative x-iection, as shown in the figue. If the magnitues of the an fiels ae. /m an. T, espectivel, what is the paticle s spee (in m/s) at t = s? () () (3) (4) 3 (5) 4 -axis 5. A positivel chage paticle with a chage to mass atio /m = C/kg is taveling to the ight along the with spee = 4 m/s. At t = an x = it encountes unifom anti-paallel electic an magnetic fiels. The magnetic fiel points in the positive x-iection an the electic fiel points in the negative x-iection, as shown in the figue. If the magnitues of the an fiels ae. /m an. T, espectivel, what is the paticle s spee (in m/s) at t = s? () () (3) (4) 3 (5) 4 -axis 6. Thee infinitel long staight wies lie in a plane an ca cuent in the same iection as shown in the figue. The top wie caies cuent I an is a istance fom the cente wie which caies cuent I. The bottom wie caies cuent 4I an is a istance fom the cente wie. What is the magnitue of the net foce on a length = /4 of the cente wie ue to the othe two wies? (Note that k = µ /4π) I I 4I () 3k I () 6k I (3) 9k I (4) k I (5) 4k I 7. Thee infinitel long staight wies lie in a plane an ca cuent in the same iection as shown in the figue. The top wie caies cuent I an is a istance fom the cente wie which caies cuent I. The bottom wie caies cuent 4I an is a istance fom the cente wie. What is the magnitue of the net foce on a length = / of the cente wie ue to the othe two wies? (Note that k = µ /4π) () 6k I () 3k I (3) 9k I (4) k I (5) 4k I I I 4I

8 8. Thee infinitel long staight wies lie in a plane an ca cuent in the same iection as shown in the figue. The top wie caies cuent I an is a istance fom the cente wie which caies cuent I. The bottom wie caies cuent 4I an is a istance fom the cente wie. What is the magnitue of the net foce on a length = 3/4 of the cente wie ue to the othe two wies? (Note that k = µ /4π) I I 4I () 9k I () 3k I (3) 6k I (4) k I (5) 4k I 9. A moveable (massless an fictionless) o with a length of =.5 metes is being move at a constant spee along two conucting ails b a constant extenalfocef ext = 3N,asshowninthefigue. Theentiesstemisimmese in a unifom constant magnetic fiel (z-axis out of the pape). If the inuce cuent in the esisto R is A, what is the magnitue of the magnetic fiel (in T)? -out R F ext () 3 () (3) (4) 4 (5) 5. A moveable (massless an fictionless) o with a length of =.5 metes is being move at a constant spee along two conucting ails b a constant extenalfocef ext = 3N,asshowninthefigue. Theentiesstemisimmese in a unifom constant magnetic fiel (z-axis out of the pape). If the inuce cuent in the esisto R is 3 A, what is the magnitue of the magnetic fiel (in T)? -out R F ext () () 3 (3) (4) 4 (5) 5. A moveable (massless an fictionless) o with a length of =.5 metes is being move at a constant spee along two conucting ails b a constant extenalfocef ext = 3N,asshowninthefigue. Theentiesstemisimmese in a unifom constant magnetic fiel (z-axis out of the pape). If the inuce cuent in the esisto R is 6 A, what is the magnitue of the magnetic fiel (in T)? -out R F ext () () 3 (3) (4) 4 (5) 5. Consie an oscillating C cicuit consisting of a capacito with C = mf, no esistance, an an unknown inucto as shown in the figue. At a cetain moment of time the chage on the capacito is 4 mc an the cuent though the inucto is A. If the maximum chage on the capacito uing the oscillations is 6 mc, what is the inuctance (in mh) of the unknown inucto? () 5 () (3) 3 (4) 8 (5) 4 C I 3. Consie an oscillating C cicuit consisting of a capacito with C = mf, no esistance, an an unknown inucto as shown in the figue. At a cetain moment of time the chage on the capacito is 4 mc an the cuent though the inucto is A. If the maximum chage on the capacito uing the oscillations is 8 mc, what is the inuctance (in mh) of the unknown inucto? C I () () 5 (3) 3 (4) 8 (5) 4

9 4. Consie an oscillating C cicuit consisting of a capacito with C = mf, no esistance, an an unknown inucto as shown in the figue. At a cetain moment of time the chage on the capacito is 4 mc an the cuent though the inucto is A. If the maximum chage on the capacito uing the oscillations is mc, what is the inuctance (in mh) of the unknown inucto? () 3 () 5 (3) (4) 8 (5) 4 C I 5. Two light bulbs have the following atings: 4W, an 6W,. If the two lights ae connecte in seies with a MF, what is the total powe issipate b the lights? () 4 () 3 (3) 36 (4) (5) Two light bulbs have the following atings: 45W, an 9W,. If the two lights ae connecte in seies with a MF, what is the total powe issipate b the lights? () 3 () 4 (3) 36 (4) (5) Two light bulbs have the following atings: 6W, an 9W,. If the two lights ae connecte in seies with a MF, what is the total powe issipate b the lights? () 36 () 4 (3) 3 (4) (5) 5 8. Initiall two isolate capacitos with capacitance C an C both ca chage. The two capacitos ae then connecte togethe in paallel (i.e., the positive plate of C connecte to the positive plate of C an the negative plate of C connecte to the negative plate of C ). If C = C, what is the chage on capacito C afte the come to euilibium? () 4/3 () 3/ (3) /3 (4) (5) 9. Initiall two isolate capacitos with capacitance C an C both ca chage. The two capacitos ae then connecte togethe in paallel (i.e., the positive plate of C connecte to the positive plate of C an the negative plate of C connecte to the negative plate of C ). If C = 3C, what is the chage on capacito C afte the come to euilibium? () 3/ () 4/3 (3) /3 (4) (5) 3. Initiall two isolate capacitos with capacitance C an C both ca chage. The two capacitos ae then connecte togethe in paallel (i.e., the positive plate of C connecte to the positive plate of C an the negative plate of C connecte to the negative plate of C ). If C = C /, what is the chage on capacito C afte the come to euilibium? () /3 () 4/3 (3) 3/ (4) (5) 3. A point paticle with chage = mc an mass M = gams entes along the cente of a paallel plate capacito () with a spee of m/s as shown in the figue. The plates of the capacito ae sepaate b a istance with one plate at = +/ an the othe at = /. If = cm an if the chage paticle hits the bottom plate of the capacito afte taveling a hoizontal istance of.4 cm insie the capacito, what is the electic potential iffeence acoss the capacito (in )? () 5, () 3, (3),5 (4),5 (5),6 v -axis

10 3. A point paticle with chage = mc an mass M = gams entes along the cente of a paallel plate capacito () with a spee of m/s as shown in the figue. The plates of the capacito ae sepaate b a istance with one plate at = +/ an the othe at = /. If = cm an if the chage paticle hits the bottom plate of the capacito afte taveling a hoizontal istance of.5 cm insie the capacito, what is the electic potential iffeence acoss the capacito (in )? () 3, () 5, (3),5 (4),5 (5),6 v -axis 33. A point paticle with chage = mc an mass M = gams entes along the cente of a paallel plate capacito () with a spee of m/s as shown in the figue. The plates of the capacito ae sepaate b a istance with one plate at = +/ an the othe at = /. If = cm an if the chage paticle hits the bottom plate of the capacito afte taveling a hoizontal istance of.8 cm insie the capacito, what is the electic potential iffeence acoss the capacito (in )? (),5 () 5, (3) 3, (4),5 (5),6 v -axis 34. A cuent of.75 A flows though a coppe wie.4 mm in iamete when it is connecte to a potential iffeence of 5. If the esistivit of coppe is.7 8 Ω m, how long is the wie (in m)? () 47.8 () 3. (3) 33.6 (4) 59.4 (5) A cuent of.75 A flows though a coppe wie.5 mm in iamete when it is connecte to a potential iffeence of 5. If the esistivit of coppe is.7 8 Ω m, how long is the wie (in m)? () 3. () 47.8 (3) 33.6 (4) 59.4 (5) A cuent of.75 A flows though a coppe wie.6 mm in iamete when it is connecte to a potential iffeence of 5. If the esistivit of coppe is.7 8 Ω m, how long is the wie (in m)? () 33.6 () 47.8 (3) 3. (4) 59.4 (5) A suae wie loop with aea A = 4. m otates about the vetical -axis at 3,6 ev/min in a unifom magnetic fiel that points in the x-iection, as shown in the figue. If the maximum emf inuce in the loop is 5, what is the magnitue of the magnetic fiel (in mt)? () 33. () 49.7 (3) 66.3 (4).6 (5) 85. -axis ω 38. A suae wie loop with aea A = 4. m otates about the vetical -axis at 3,6 ev/min in a unifom magnetic fiel that points in the x-iection, as shown in the figue. If the maximum emf inuce in the loop is 75, what is the magnitue of the magnetic fiel (in mt)? () 49.7 () 33. (3) 66.3 (4).6 (5) 85. -axis ω

11 39. A suae wie loop with aea A = 4. m otates about the vetical -axis at 3,6 ev/min in a unifom magnetic fiel that points in the x-iection, as shown in the figue. If the maximum emf inuce in the loop is, what is the magnitue of the magnetic fiel (in mt)? () 66.3 () 33. (3) 49.7 (4).6 (5) 85. -axis ω 4. Consie the R cicuit shown in the figue which consists of an 8 olt MF, an inucto, = 4 H, an two esistos. Afte the switch is close, what is the stoe eneg in the inucto (in J) at the instant the cuent though the Ω esisto is eual to A? 8 R = Ω = 4H R =4 Ω () 4.5 () 8. (3) 4.5 (4) 7. (5). 4. Consie the R cicuit shown in the figue which consists of an 8 olt MF, an inucto, = 4 H, an two esistos. Afte the switch is close, what is the stoe eneg in the inucto (in J) at the instant the cuent though the Ω esisto is eual to A? 8 R = Ω = 4H R =4 Ω () 8. () 4.5 (3) 4.5 (4) 7. (5). 4. Consie the R cicuit shown in the figue which consists of an 8 olt MF, an inucto, = 4 H, an two esistos. Afte the switch is close, what is the stoe eneg in the inucto (in J) at the instant the cuent though the Ω esisto is eual to 3 A? 8 R = Ω = 4H R =4 Ω () 4.5 () 4.5 (3) 8. (4) 7. (5). 43. A tain is tavelling (in a vacuum) along the at spee, as shown in the figue. Thee is a light souce at est on the tain that emits light in the negative x-iection. An obseve at est on the tain measues the wavelength of the light to be 5 nm an the spee of the light to be c. An obseveat est on the sie of the tack an sees the tain pass him at spee =.c, whee c is the spee of light in a vacuum. What is the wavelength of light (in nm) measue b the obseve on the sie of the tack afte the tain has passe? -axis ight souce () 6.4 () (3). (4) 48. (5) In the pevious poblem, what is the spee of light measue b the obseve on the sie of the tack afte the tain has passe? () c ().8c (3).6c (4).4c (5).c

12 45. A tain is tavelling (in a vacuum) along the at spee, as shown in the figue. Thee is a light souce at est on the tain that emits light in the negative x-iection. An obseve at est on the tain measues the wavelength of the light to be 5 nm an the spee of the light to be c. An obseveat est on the sie of the tack an sees the tain pass him at spee =.4c, whee c is the spee of light in a vacuum. What is the wavelength of light (in nm) measue b the obseve on the sie of the tack afte the tain has passe? -axis ight souce () () 6.4 (3). (4) 48. (5) In the pevious poblem, what is the spee of light measue b the obseve on the sie of the tack afte the tain has passe? () c ().8c (3).6c (4).4c (5).c 47. A tain is tavelling (in a vacuum) along the at spee, as shown in the figue. Thee is a light souce at est on the tain that emits light in the negative x-iection. An obseve at est on the tain measues the wavelength of the light to be 5 nm an the spee of the light to be c. An obseveat est on the sie of the tack an sees the tain pass him at spee =.6c, whee c is the spee of light in a vacuum. What is the wavelength of light (in nm) measue b the obseve on the sie of the tack afte the tain has passe? -axis ight souce (). () 6.4 (3) (4) 48. (5) In the pevious poblem, what is the spee of light measue b the obseve on the sie of the tack afte the tain has passe? () c ().8c (3).6c (4).4c (5).c 49. An obseve at est in the O-fame measues the wavelength of the light fom a comet that is tavelling at a constant spee. The obseve measues wavelength λ towa when the comet is tavelling aiall towa him an wavelengthλ awa when the comet is tavellingaiallawafom him. If λ awa = λ towa, what is the spee of the comet? (Note that c is the spee of light in a vacuum.) at est () c/3 () c/ (3) 3c/5 (4) c/4 (5) 3c/4 Awa Towa at est 5. An obseve at est in the O-fame measues the wavelength of the light fom a comet that is tavelling at a constant spee. The obseve measues wavelength λ towa when the comet is tavelling aiall towa him an wavelengthλ awa when the comet is tavellingaiallawafom him. If λ awa = 3λ towa, what is the spee of the comet? (Note that c is the spee of light in a vacuum.) at est () c/ () c/3 (3) 3c/5 (4) c/4 (5) 3c/4 Awa Towa at est 5. An obseve at est in the O-fame measues the wavelength of the light fom a comet that is tavelling at a constant spee. The obseve measues wavelength λ towa when the comet is tavelling aiall towa him an wavelengthλ awa when the comet is tavellingaiallawafom him. If λ awa = 4λ towa, what is the spee of the comet? (Note that c is the spee of light in a vacuum.) at est () 3c/5 () c/3 (3) c/ (4) c/4 (5) 3c/4 Awa Towa at est

13 5. A small unewate pool light is. m below the suface of a swimming pool. What is the aea (in m ) of the cicle of light on the suface, fom which light emeges fom the wate? (Use n wate = 4/3 an n ai =.) () 5.8 () 7.9 (3).34 (4) 4.4 (5) A small unewate pool light is.4 m below the suface of a swimming pool. What is the aea (in m ) of the cicle of light on the suface, fom which light emeges fom the wate? (Use n wate = 4/3 an n ai =.) () 7.9 () 5.8 (3).34 (4) 4.4 (5) A small unewate pool light is.6 m below the suface of a swimming pool. What is the aea (in m ) of the cicle of light on the suface, fom which light emeges fom the wate? (Use n wate = 4/3 an n ai =.) ().34 () 5.8 (3) 7.9 (4) 4.4 (5) Two light waves tavel in ai with wavelength 5 nm, an the ae initiall in phase. ach passes though a block of length befoe passing back into the ai. One tavels though glass with inex of efaction n =.7, an the othe passes though ice with inex of efaction n =.3. What is the minimum value of (in nm) fo which the waves will unego maximum estuctive intefeence? () 65 () 7 (3) 75 (4) 48 (5) Two light waves tavel in ai with wavelength 56 nm, an the ae initiall in phase. ach passes though a block of length befoe passing back into the ai. One tavels though glass with inex of efaction n =.7, an the othe passes though ice with inex of efaction n =.3. What is the minimum value of (in nm) fo which the waves will unego maximum estuctive intefeence? () 7 () 65 (3) 75 (4) 48 (5) Two light waves tavel in ai with wavelength 6 nm, an the ae initiall in phase. ach passes though a block of length befoe passing back into the ai. One tavels though glass with inex of efaction n =.7, an the othe passes though ice with inex of efaction n =.3. What is the minimum value of (in nm) fo which the waves will unego maximum estuctive intefeence? () 75 () 65 (3) 7 (4) 48 (5) Two ientical conveging lenses each with a focal length of m ae place.5 m apat. What is the oveall magnification of the two-lens sstem fo an object place.5 m awa fom the font lens? () 4 () (3) (4) 4 (5) 59. Two ientical conveging lenses each with a focal length of m ae place. m apat. What is the oveall magnification of the two-lens sstem fo an object place.5 m awa fom the font lens? () () 4 (3) (4) 4 (5) 6. Two ientical conveging lenses each with a focal length of m ae place m apat. What is the oveall magnification of the two-lens sstem fo an object place.5 m awa fom the font lens? () () 4 (3) (4) 4 (5)

14 TH FOOWING USTIONS, NUMRD IN TH ORDR OF THIR APPARANC ON TH AO IST, HA N FAGGD AS CONTINUATION USTIONS: FOOWING GROUPS OF USTIONS WI SCTD AS ON GROUP FROM ACH TYP TYP # S # S # S 3 TYP # S 4 # S 5 # S 6 TYP 3 # S 7 # S 8 # S 9 TYP 4 # S # S # S TYP 5 # S 3 # S 4 # S 5 TYP 6 # S 6 # S 7 # S 8 TYP 7 # S 9 # S # S TYP 8 # S # S 3 # S 4 TYP 9 # S 5 # S 6 # S 7 TYP # S 8 # S 9 # S 3 TYP # S 3 # S 3 # S 33 TYP # S 34 # S 35 # S 36 TYP 3 # S 37 # S 38 # S 39 TYP 4 # S 4 # S 4 # S 4 TYP 5 # S # S # S TYP 6 # S 49 # S 5 # S 5 TYP 7 # S 5 # S 53 # S 54 TYP 8 # S 55 # S 56 # S 57

15 TYP 9 # S 58 # S 59 # S 6