SAMPLE USEFUL INFORMATION: Acceleration due to gravity, gg 9.80 m s 2. Avogadro s number, NN AA particles

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2 USFUL INFORMTION: cceleratin due t gravity, gg 9.80 m s vgadr s number, NN particles ml Universal gas cnstant, RR J K 1 ml 1 Gravitatinal cnstant, GG N m kg ulmb cnstant, kk N m Magnitude f charge f electrn, ee Mass f electrn, mm ee kg Mass f prtn, mm pp kg Mass f neutrn, mm nn kg Speed f light, cc m s 1 Planck s cnstant, h J s tmic mass unit, uu kg SMPL U 018 PHY / 0

3 1. displacement vectr with a magnitude f 0 m culd have perpendicular cmpnents with magnitudes f 0 m and 0 m m and m 1 m and 16 m 1 m and 80 m 16 m and 8 m. What is the center f gravity f an bject? the gemetrical center f the bject the pint abut which the ttal trque is zer the pint at which the weight f the bject may be cnsidered t act the pint thrugh which gravity acts the intersectin f the vertical symmetrical line and the hrizntal symmetrical line 3. The fllwing graph shws hw the hrizntal displacement f a car mving n a flat grund changes with time fr part f its jurney. n imprvised accelermeter, used t measure the acceleratin f the car, is made by sandwiching a rubber ring between the tw glass plates and intrducing sme clured water insider the ring. The accelermeter is subsequently fastened at the dr f the car. iagram crrespnds t pint X n the graph. S PL Which diagram shws the angle f water surface in the accelermeter at pint Y? Nne f the abve U 018 PHY / 0 3

4 4. n bject starts frm rest and falls freely fr 40 m near the surface f a planet. If the time f fall is 4 s, what is the magnitude f the acceleratin due t gravity n the planet? 0 m/s 5.0 m/s m/s 0 m/s 40 m/s 5. mtrist travelling at ms -1 can bring his car t rest in a braking distance f m. In what distance culd he bring the car t rest frm a speed f 30 ms -1 using the same braking frce? 17 m 30 m 5 m 90 m 98 m 6. Newtn s third law cncerns the frces f interactin between tw bdies. Which f the fllwing statements relating t the third law is nt crrect? The tw frces must be f the same type. The tw frces must act n different bdies. The tw frces are always ppsite in directin. The tw frces are equal and ppsite s the bdies are in equilibrium. Nne f the abve. SMPL 7. In a Frmula One race, Sebastian Vettel driving the Ferrari race car has t make a pit-stp t re-fuel the petrl tank. fter the re-fueling, he starts frm rest with a cnstant acceleratin f 11.0 ms - and takes 3.5 s t enter the main speedway frm the pit area. t the instance Sebastian enters the main speedway, anther race car n the speedway, driven by Hamiltn, traveling at a cnstant velcity f 69.4 ms -1 passes Sebastian s car. What is the ttal time required fr Sebastian s car t catch up with Hamiltn frm the time he cmpletes the re-fueling? ssume that Sebastian maintains a cnstant acceleratin thrughut this time. 5.6 s 9.1 s 1.6 s 16.1 s 18. s U 018 PHY / 0 4

5 8. Tw satellites in space cllide inelastically. What happens t the kinetic energy and mmentum? kinetic energy mmentum cnserved cnserved cnserved reduced reduced cnserved reduced reduced reduced increased 9. cyclist is riding at a steady speed n a level rad. ccrding t Newtn s third law f mtin, what is equal and ppsite t the backward push f the back wheel n the rad? the frce exerted by the cyclist n the pedals the frward push f the rad n the back wheel the tensin in the cycle chain the ttal air resistance and frictin frce the frce prvided by the break pads n the wheels.. What is meant by the weight f an bject? the gravitatinal field acting n the bject the gravitatinal frce acting n the bject the mass f the bject multiplied by gravity the bject s mass multiplied by its acceleratin the bject s mass multiplied by its velcity SMPL 11. fighter-bmber flies twards a target at a speed f 750 kmh -1. t a height f 500 m abve the grund, it releases a 150-kg bmb while diving at an angle f 0 belw the hrizntal. Hw far ahead f the target hrizntally must the bmb be released? 173 m 13 m 3013 m 3813 m 4813 m 1. prjectile will attain its largest height if it is fired at an angle f frm the hrizntal. U 018 PHY / 0 5

6 13. rller caster f mass m mves in a vertical circle f radius r. The rller caster will be up-ide-dwn when it is at the highest pint f the circle. t what minimum speed v must the rller caster be travelling at the bttm f the circle s that the ride will be safe? rg rg 3 rg 4 rg 5 rg 14. ball f mass 00 g is prjected up a smth inclined plane f length 0.50 m, at an angle 30 abve the hrizntal, with an initial speed f.5 ms -1. The ball subsequently leaves the ther end f the plane and prceeds with a prjectile mtin. MPL ssuming that the air resistance is negligible, what is the minimum f the kinetic energy fr the whle flight? 0 J 0. J 0.13 J 0.47 J 0.6 J U 018 PHY / 0 6

7 15. mdel car is released frm rest at a height h n a frictinless track. The car ges arund the lp f diameter withut drpping frm the track. What is the minimum pssible value f the initial height h required fr the car t remain n the track while ging arund the lp? SMPL 16. lead pellet is sht vertically upwards int a clay blck that is statinary at the mment f impact but is able t rise freely after the impact. The pellet hits the blck with an initial velcity f 00 ms -1. It embeds itself in the blck and des nt emerge. Hw high abve its initial psitin will the blck rise? 5.1 m 5.6 m m 14 m m U 018 PHY / 0 7

8 17. car mass f 1. 3 kg travels alng a hrizntal rad at a speed f ms -1. It then accelerate at 0.0 ms -. t the time it begins t accelerate, the ttal resistive frce acting n the car is 160 N. What ttal utput is develped by the car as it begins the acceleratin? 0.80 kw 1.6 kw.4 kw 4.0 kw 5.6 kw 18. snker ball f mass m travels at a speed v twards the side f a snker table. The ball strikes the side f the table at an angle f 30 as shwn. The time f cntact between the ball and the side is t. What is the expressin fr the average frce acting n the ball? Plan View mv t mv cs30 t mv cs30 t mv csc30 t mv sin 30 t SM U 018 PHY / 0 8

9 19. The figure belw shws frces acting n a piece f square cardbard f negligible mass n a hrizntal plane. The cardbard has a length f 5.0 cm n each side. Which f the fllwing statements is pssibly true? The cardbard is nt in equilibrium. The cardbard is in rtatinal equilibrium. The cardbard is nt in translatinal equilibrium. The cardbard will rtate in an anticlckwise directin. The cardbard will underg linear acceleratin. 0. ssuming heat capacity f a g f water t be 4 J K, heat required t raise its temperature frm 5 t 35 wuld be 4 J 40 J 400 J 4000 J Nne f abve SMPL 1. When the pressure f an ideal gas is increased at cnstant vlume, the average kinetic energy f the gas mlecules may either increase r decrease, depending n whether r nt the prcess is carried ut adiabatically. may r may nt change, but insufficient infrmatin is given t make such a determinatin. des nt change. increases. decreases. U 018 PHY / 0 9

10 . One junctin X f a thermcuple is placed in melting ice at 73 K and the ther junctin Y in steam at 373 K. The e.m.f. measured is.0 mv. Junctin Y is then transferred t a bath at a temperature f 398 K. ssuming that the variatin f e.m.f. with temperature difference is linear, the e.m.f., in mv, recrded will nw be brass bar and a steel bar, each m lng, are at a temperature f 0. ach bar is placed at that temperature between rigid walls m apart. The crss-sectinal areas fr the brass and steel bars are m and m, respectively. The cefficient f linear expansin and Yung mdulus f the tw materials are given in the table belw. efficient f Linear Yung mdulus xpansin rass K Pa Steel K 11.0 Pa SMPL The temperature is raised until the cmbined frce exerted by the tw bars is 1.8 MN. The temperature at which this ccurs, in, is clsest t U 018 PHY / 0

11 4. heat-cnducting rd, 1. m lng, is made f an aluminium sectin, 0.0 m lng, and a cpper sectin, 0.90 m lng. th sectins have a crss-sectinal area f m. The aluminium end and the cpper end are maintained at temperatures f and 50, respectively. The 1 thermal cnductivities f aluminium and cpper are 05 W m 1 K and W m 1 K, respectively. The temperature f the aluminium-cpper junctin in the rd, in, is clsest t The speed f light in a material is 0.50c. What is the critical angle f a light ray at the interface between the material and a vacuum? n electrmagnetic wave, passing frm medium X t medium Y, underges a 30% increase in wave speed. If the angle f incidence at the interface f X and Y is 45, what is the angle f refractin in medium Y? SMPL 7. Three flat layers f transparent material are stacked upn ne anther. The tp layer has index f refractin n 1, the middle n and the bttm ne n 3. If n 1 > n > n 3, and a ray f light in air strikes the tp layer, at which surface given can ttal internal reflectin ccur first? the tp surface the surface between materials with indices n 1 and n the surface between materials with indices n and n 3 the bttm surface Ttal internal reflectin cannt ccur at any f these surfaces. U 018 PHY / 0 11

12 8. cnvex lens has a fcal length f. n bject is placed between infinity and f frm the lens alng a line perpendicular t the center f the lens. The image is lcated at what distance frm the lens? farther than f f f between f and f between the lens and f 9. Parallel water waves f wave length 0 m strike a straight sea wall. The wavefrnts make an angle 30 with the wall. What is the difference in phases between the waves at tw pints m apart alng the wall? Nne f the abve. 30. Tw narrw slits, 0.30 mm apart, are illuminated by a beam f light f wavelength 700 nm. n interference pattern is bserved n a screen nrmal t the beam and 3.0 m frm the slits. The distance in mm between adjacent dark lines n the screen is SMPL Light f wavelength 40 nm is incident n a diffractin grating f 3.8 lines per metre. Which ne f the fllwing is the highest diffractin rder which can be bserved? U 018 PHY / 0 1

13 3. The least distance between tw pints f a prgressive transverse wave which have a phase difference f π 3 rad is m. If the frequency f the wave is 500 Hz, what is the speed f the wave? 4 m/s 5 m/s 75 m/s 150 m/s 300 m/s 33. Tw cnducting spheres and, f radii r and r, carry charges + and + respectively. The centres f the spheres are a distance d apart with d slightly greater than r + r. Which f the fllwing statements abut the electrstatic frces F between the spheres is true? F < 4πε0d F = 4πε0d F > 4πε0d F = 4πε0 ( d + r + r ) F < 4πε0 ( d + r + r ) SMPL 34. The electrstatic ptential at a distance f 150 mm frm an islated pint 4 charge, in vacuum, is 6.0 V. The electric field, in V/m, at the same pint is U 018 PHY / 0 13

14 35. Fur pint charges are arranged at the crners f a square f length 3 m as shwn. + N The electric field at the centre f the square is 9πε 9πε t the ast t the West t the ast 9πε t the West 9πε n electrn is emitted frm an electrn gun with a speed f 3.0 m s. It mves twards a metal grid which is psitined at.0 cm away frm the gun. The grid is maintained at a ptential f 0 V with respect t the electrn gun. What is the speed f the electrn as it reaches the grid? m s m s m s m s m s SMPL µ F capacitr has a ptential difference f 5.0 V applied acrss its plates. If the ptential difference acrss its plates is increased t 8.0 V, hw much additinal energy des the capacitr stre? 36 µ J 50 µ J 78 µ J 130 µ J U 018 PHY / 0 14

15 160 µ J 38. Wire f resistivity ρ and crss-sectinal area is frmed int a square f side b, as shwn belw. X b b b Y b The resistance between tw vertices f the square, X and Y, is 3 ρb 4 ρb 4 ρb 4 ρb 4 3 ρb 39. The battery is discnnected frm a series R circuit after the capacitr is fully charged and is replaced by an pen switch. When the switch is clsed, the capacitr des nt allw current t pass. the current stps in the resistr. the ptential difference acrss the resistr is always greater than the ptential difference acrss the capacitr. the ptential difference acrss the resistr is always less than the ptential difference acrss the capacitr. the ptential difference acrss the resistr is always equal t the ptential difference acrss the capacitr. SMPL 40. In defining the ampere it is said that the frce per metre between tw thin, infinitely lng parallel straight wires in vacuum ne metre apart, is 7 N m when the current in each wire is 1. The frce per metre, in N/m, when the wires each carry currents f 3 and are m apart is U 018 PHY / 0 15

16 neutral sub-atmic particle is at rest in a unifrm magnetic field f magnitude. It splits int tw particles each f mass m, ne f which has a psitive charge +. The particles then mve with velcities perpendicular t the magnetic field. fter what time will the particles cllide? 5mπ mπ 3mπ mπ mπ 4. flat search cil cntaining 0 turns each f area.0 m is cnnected t a galvanmeter. The ttal resistance f the circuit is 50 Ω. The cil is placed such that its plane is nrmal t a magnetic field f magnitude 0.5 T. What is the quantity f charge induced when the cil is turned ver thrugh an angle f 90? SMPL 43. circular lp f wire is placed in a unifrm magnetic field f 1. T that is nrmal t the plane f the lp. The lp shrinks frm a radius f 0.0 m t a radius f 0. m in s, at a rate which generates a steady electrmtive frce (emf). The induced emf is 0 V 0.75 V 1.1 V.3 V 3.0 V U 018 PHY / 0 16

17 44. slenid with a large number f turns f wire is cnnected in series with an ammeter and a battery. n irn rd is passed thrugh the slenid at cnstant speed. Which graph shws the variatin with time t f the reading I f the ammeter? SMP Nne f the abve. U 018 PHY / 0 17

18 45. The graph shws a rectangular wavefrm with a peak current f. urrent/ Time T give the same rt-mean-square current as the wavefrm shwn, a sinusidal current f the same frequency will have a peak value f sinusidal current f peak value I 0 passes thrugh a resistr R with a dide cnnected in series with it. The average rate f heat dissipated in R is I 0 R 0.5I 0 R 0.35I 0 R 0.50I 0 R 0.71I 0 R SMPL 47. In a nuclear reactin, energy equivalent t The energy released is apprximately kg f matter is released J J J J J U 018 PHY / 0 18

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