Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively. Find the rati r B / r A if the mass f sphere B is five times the mass f sphere A. A) 1.7 B). C).7 D) 1. E). m B = 5m A sv B = 5sV A 4π R B = 5 4π R A R B = (5) 1 R A R B R A = 5 1 = 1.71 Q. The psitin x f a particle is given by H x = Rt + t R where x is in meters and t is in secnds. The dimensin f H is A) B) C) D) E) LT LT 5 LT ML T ML T 5 [H] = L [R] T, [R] = L T = LT = L LT T = L T 5 c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: Q. Q4. The velcity f a train is 8. km/h, due west. One and a half hur later its velcity decreases t 65. km/h, due west. What is the train s average acceleratin? a avg = A) 1. km/h due east B) 1. km/h due west C) 4. km/h due west D) 4. km/h due east E) 5. km/h due east 65 8 1.5 = 1 km/h due west A ball mves in a straight line alng the x-axis and Figure 1 shws its velcity as a functin f time t. What is the ball average velcity and average speed, respectively, ver a perid f. s. A). m/s,. m/s B). m/s,. m/s C). m/s,. m/s D) 1.66 m/s,. m/s E). m/s, 1.66 m/s Average Velcity = x t = 1 Figure 1 = 4 =. m/s Average Speed = s t = + 1 = 7 =. m/s c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: Q5. The psitin f an bject mving alng the x-axis is given by x = 6. + 6. t. t, where x is in meters and t in secnds. Which statement abut this bject is crrect? A) The bject is mmentarily at rest at t = 1. s. B) The bject psitin is negative at t = s. C) The acceleratin f the bject is zer at t = s. D) The acceleratin f the bject is psitive at all times. E) The bject is mmentarily at rest at t =. s. x = 6 + 6t t m v = dx = 6 6t m/s df Fr v =, 6 6t =, Then v =, at t = 1 sec a = dv = 6 m/s dt x(t = ) = +6. m Q6. A rck is thrwn vertically upward frm grund level at time t =. s. At t =1.5 s it passes the tp f a tall twer, and then 1. s later it reaches its maximum height. What is the height f the twer? A) 6 m B) 6 m C) 6 m D) 16 m E) m Twer Height H = v iy t 1 gt but v fy = v iy gt fr maximum heigh v fy =, and t = 1.5 + 1. =.5 sec then v iy = g t = 9.8.5 = 4.5 m/s H = v iy t 1 gt v iy = 4.5 m/s, t = 1.5 sec H = 4.5 1.5 1 9.8 (1.5) H = 5.7 m = 6 m c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 4 Q7. Q8. A man walks 5 m in a directin 7 nrth f east at 5. m/s, then 6 m suth at 4. m/s. Hw lng wuld it take him t get back t his starting pint at 5. m/s by the shrtest path? A) 1 s B) 15 s C) s D) 5. s E).5 s x = 5cs7 = 9.9 m y = 5 sin 7 6 =.9 6 = 9.9 r = ( x) + ( y) = 49.9 m, t = r v = 49.9 = 9.98 sec 5 Vectr A has a magnitude f 5. m and makes an angle f 7. with the psitive x axis. Find a vectr B that is in the directin ppsite t vectr A and is ne fifth the magnitude f A. B = A 5 A) (5.59 m) iˆ (4.1m) ĵ B) (5.59 m) iˆ + (4.1 m) ĵ C) (.798 m) iˆ (.6 m) D) ( 1.56 m) iˆ (5.6 m) ĵ ĵ E) (.798 m) iˆ + (.6 m) A = 5cs7ı + 5sin7ȷ A = 7.95ı + 1.6ȷ B = 1 (7.95ı + 1.6ȷ ) 5 = 5.59ı 4.1ȷ ĵ c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 5 Q9. If A = iˆ + ĵ, B = i ˆ ĵ and C = i ˆ + ĵ, find (A xb ). C. A) B) 6 C) +6 D) E) + kˆ iˆ C = ı + ȷ ; D = A B = k D. C = Q1. The scalar prduct f vectrs A and B is 6. and the magnitude f their vectr prduct is 9.. Find the angle between these tw vectrs. A) 56. B) 4. C).4 D) 7.5 E) 9. ABcsθ = A. B = 6, A B = 9. = ABsinθ tanθ = A. B A B = 9 6 = 1.5 θ = tan 1 (1.5) = 56. Q11. The psitin f a particle is given by r = (4t t ) i ˆ + t ĵ, where r is in meters and t in secnds. Find the average acceleratin (in m/s ) f the particle in the time interval between t = s and t = 4 s. A) iˆ +18 ĵ B) 4 iˆ 6 ĵ C) 5 iˆ 1 ĵ D) 7 iˆ 1 ĵ E) 1 iˆ 6 ĵ v = dr dt = (4 t)ı + t ȷ v(t = s) = (4 4)ı + 1ȷ = 1ȷ v(t = 4s) = (4 8)ı + 48ȷ = 4ı + 48ȷ a avg = v 4ı + 48ȷ 1ȷ = = t 4ı + 6ȷ = ı + 18ȷ c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 6 Q1. A prjectile is thrwn frm the grund int the air with an initial speed v. Its velcity, 1.5 s after it was thrwn, is 4. m/s making an angle.4 abve the hrizntal. Determine the initial velcity v f the prjectile. A) 51. m/s at 44.7 abve the hrizntal B) 4.1 m/s at 4. abve the hrizntal C) 1.6 m/s at 49. abve the hrizntal D).5 m/s at.5 abve the hrizntal E) 1. m/s at 54.5 abve the hrizntal v y (t = 1.5 sec) = vsinθ = 4. sin(.4) = 1.4 m/s v x = vcsθ = 4. cs(.4) = 6.48 m/s v y = v y + gt = 1.41 + 9.8 1.5 = 6.11m/s v = v x + v y = 6.11 + 6.48 = (51. m)/s, θ = tan 1 v y = tan 1 6.11 = 44.7 v x 6.48 Q1. A.15 kg ball, attached t the end f a string, is revlving unifrmly in a hrizntal circle f radius.6 m. The ball makes 1. revlutins in 5. secnds. Calculate the centripetal acceleratin f the ball? A) 94.8 m/s B) 5.7 m/s C) 1.6 m/s D) 9.81 m/s E) zer a = v R ; v = πr T π.6 v =.5 a = (7.54).6 ; T = 5 sec 1 rev = 1 sec = 7.54 m/s = 94.8 m/s c--n-15-s--e-1-fg-1-f-
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 7 Q14. A bat is t travel frm pint A t pint B directly acrss a river. The water in the river flws with a velcity f 1. m/s tward the west, as shwn in Figure. If the speed f the bat in still water is 1.85 m/s, at what angle frm the nrth must the bat head? Figure # A) 4.4 east f nrth B). west f nrth C) 1.5 east f nrth D) 9. west f nrth E) 55. west f nrth θ = sin 1 1. 1.85 = 4.44 f nrth θ V=1. m/s 1.85 m/s Q15. Which ne f the curves shwn in Figure best represents the vertical cmpnent f the velcity v y versus time t fr a prjectile fired at an angle f 45 abve the hrizntal? Figure A) AE B) AB C) OC D) DE E) AF v y = v iy gt y = g, line with ve slpe t c--n-15-s--e-1-fg-1-f-