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UNIVERSITY ENTRANCE EXAMINATION PHYSICS Duration : 2 hours Please read the following instructions carefully. 1. This paper is made up of 50 Multiple-Choice questions and comprises TWENTY (20) printed pages. 2. Do not write on the question paper. 3. Answer all questions and indicate your answers on the answer sheet provided. Marks will not be deducted for wrong answers. 4. Do not take any paper, including the question paper or unused answer sheets, out of the examination hall. 1 USEFUL INFORMATION: Acceleration due to gravity, 𝑔 ≈ 9.80 m s −2 Avogadro’s number, 𝑁𝐴 ≈ 6.022 × 1023 particles⁄mol Universal gas constant, 𝑅 ≈ 8.314 J K −1 mol−1 Gravitational constant, 𝐺 ≈ 6.673 × 10−11 N m2 kg −2 Coulomb constant, 𝑘 ≈ 8.99 × 109 N m2 C−2 Magnitude of charge of electron, 𝑒 ≈ 1.602 × 10−19 C Mass of electron, 𝑚𝑒 ≈ 9.109 × 10−31 kg Mass of proton, 𝑚𝑝 ≈ 1.673 × 10−27 kg Mass of neutron, 𝑚𝑛 ≈ 1.675 × 10−27 kg Speed of light, 𝑐 ≈ 2.998 × 108 m s −1 Planck’s constant, ℎ ≈ 6.626 × 10−34 J s Atomic mass unit, 𝑢 ≈ 1.661 × 10−27 kg 2 1. What is the SI unit for acceleration? A B C D E 2. kg J N m/s m/s2 A uniform beam in a symmetrical roof structure has a weight of 180 N. It is supported evenly in two places X and Y at a distance 3.0 m apart. A load is placed on the beam a distance of 0.80 m from X. The support provided by Y is 220 N. What is the value of the load? A B C D E 3. N N N N N An unbalanced force of 40 N keeps a 5-kg object traveling in a circle of radius 2 m on a horizontal plane. What is the speed of the object? A B C D E 4. 270 490 520 830 980 8 m/s 2 m/s 16 m/s 4 m/s 6 m/s A student is standing in an elevator that is accelerating upward. The force that the student exerts on the floor of the elevator must be A B C D E less than the weight of the student when at rest. greater than the weight of the student when at rest. less than the force of the floor on the student. greater than the force of the floor on the student. The answer is not certain because of insufficient information. 3 5. An object falls freely with constant acceleration a from above three light gates. It is found that it takes a time t to fall between the first two light gates a distance of s1 apart. It then takes an additional time, also t, to fall between the second and third light gates a distance s2 apart. What is the acceleration in terms of s1, s2 and t? A B C D E 6. s2 s1 t2 s2 s1 2t 2 2s 2 s1 3t 2 2s 2 s1 t2 4s 2 s1 t2 Two cars, initially next to each other and at rest, accelerate in the same straight line at different uniform rates. After 3 s, they are 12 m apart. If they continue to accelerate at the same rate, how far apart will they be 6 s after they started? A B C D E 18 24 36 48 60 m m m m m 4 7. A meteorite falls freely towards the center of an isolated spherical planet of radius R. When it reaches the surface of the planet, its acceleration is gs. What is its acceleration when at a height 2R above the surface? A B C D E 8. A car accelerates uniformly from rest along a level road. The effects of air resistance on the car are negligible. The car travels 12 m in the time between 1 s and 2 s after starting. How far does it travel in the time between 3 s and 4 s after starting? A B C D E 9. 1 gs 9 1 gs 4 1 gs 3 1 gs 2 3 gs 4 28 35 48 64 76 m m m m m A stone is dropped from a bridge. What happens to the magnitude of the acceleration and the speed of the stone as it falls? [Neglect any friction.] A B C D E Both acceleration and speed increase. Both acceleration and speed remain the same. Acceleration increases and speed decreases. Acceleration remains the same and speed increases. The answer is uncertain due to insufficient information. 5 10. A stone is thrown upwards from a point at the edge of a cliff. After the stone has reached its maximum height, it falls past the cliff edge to the beach, as shown. The initial vertical component of the velocity of the stone is 10 ms-1. The time taken between the stone passing the edge of the cliff on its way down and hitting the beach is 1.2 s. Ignoring air resistance, what is the height of the cliff? A B C D E 11. 5m 7m 12 m 19 m 26 m A wire is stretched elastically by a force of 200 N, causing an extension of 4.00 mm. The force is then steadily increased to 250 N. The wire still behaves elastically. How much extra work is done in producing the additional extension? A B C D E 0.225 J 0.250 J 225 J 250 J 270 J 6 12. A constant force F is applied to a stationary object of mass m on a frictionless surface. A constant acceleration increases the velocity of the object to some value v in a time t. It covers a distance s during this time. Which value of kinetic energy is given to the object? A Fst B Fv C Fs D ms 2t ms 4t E 13. A stone of mass m moves radially away from Earth. For a small distance x above the Earth’s surface, the variation with x of the stone’s gravitational potential energy Ep is shown as follows: At point P, a distance d from Earth, the potential energy of the stone is E and the rate of change of potential energy with distance is R. What is the force acting on the stone? A B C D E E d mE d mR 0.5R R 7 14. 15. An object of mass m is travelling with velocity v. Which equation gives the momentum p of the object in terms of either m or v and its kinetic energy Ek ? 2Ek m A p B p 2Ek v C p D p Ek m E p 2Ek m 2Ek d v The diagram shows two spheres of masses 2 kg and 3 kg moving at constant speed along a straight line towards one another. The speeds of the spheres are 4 ms-1 and 6 ms-1 respectively. The spheres collide elastically. Which statement explains why the spheres cannot come to rest at the same time? A B C D E 16. The impulses during the collision are not equal and opposite. The masses of the two spheres are not equal. The momenta of the spheres are not equal and opposite. They do not stick together after the collision. The speeds of the spheres are not equal. What is the mean speed and the mean angular velocity of the Earth in its orbit around the Sun? (The mean radius of the orbit is 1.50 x 1011 m.) A B C D E Speed / m s-1 2.99 x 104 2.99 x 104 1.09 x 107 1.09 x 107 2.99 x 107 Angular Velocity / rad s-1 1.99 x 10-7 1.72 x 10-2 1.72 x 10-2 7.27 x 10-5 7.27 x 10-5 8 17. A stone of mass m is attached to a string. The stone is rotating in a vertical circle of radius r with a constant angular speed as shown. The acceleration of free fall is g. What is the variation in magnitude of the tension in the string during one revolution of the stone? A B C D E 18. zero 2mg mr 2 2mr 2 4mr 2 The motor M in a crane is used to lift a total mass of 1400 kg through a height of 2.0 m at a constant speed of 1.6 ms-1. The motor is 20% efficient. What is the minimum input power to motor M? A B C D E 11 kW 22 kW 110 kW 140 kW 180 kW 9 19. The diagram shows a ball which has been thrown and is being acted on by air resistance. Which labelled arrow shows the direction of the resultant force when the ball is located at the highest point of its flight as shown in the following figure? 20. An immersion heater takes time T1 to raise the temperature of a mass M of a liquid from a temperature t1 to its normal boiling point t2. In a further time T2, a mass m of the liquid is vaporized. If the specific heat capacity of the liquid is c and heat losses to the atmosphere and to the containing vessel are ignored, the specific latent heat of vaporization is A Mct 2 t1 T2 mT1 B mct 2 t1 T2 MT1 C Mct1T2 mT1 D mT1 Mct 2 t1 T2 E mT1 Mct1T2 10 21. Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t) II y = 0.15 sin(6x + 42t) III y = 0.13 cos(6x + 21t) IV y = -0.23 sin(3x - 42t) Which of these waves have the same period? A B C D E 22. Consider a closed pipe of length L. What are the wavelengths of the three lowest tones produced by this pipe? A B C D E 23. I and III, and also II and IV I and IV, and also II and III I and II, and also III and IV All of them have the same period. They all have different periods. 16L, 4L, L 4L, 2L, L 2L, L, L/2 2L, L, 2L/3 4L, 4L/3, 4L/5 Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s. A B C D E 211 256 422 512 674 Hz Hz Hz Hz Hz 11 24. 25. Two charges, Q1 and Q2, are separated by a certain distance R. If the magnitudes of the charges are doubled and their separation is also doubled, then what happens to the electrical force between these two charges? A B It is doubled. It changes by a factor of 3. C D E It is reduced by a factor of It is quadrupled. It remains the same. Two point charges of magnitudes +7.00 μC, and -9.00 μC are placed along the x-axis at x = 0 cm and x = 40.0 cm, respectively. Where must a third charge be placed along the x-axis so that it does not experience any net force because of the other two charges? A B C D E 26. 2. 0.200 m 2.99 m -0.187 m -2.99 m 0.187 m A positive point charge +q is located at each of the three vertices A, B, and C of an equilateral triangle ABC as shown. Each side of the triangle is of length a. A point charge Q (that may be positive or negative) is placed at the mid-point between B and C. q A a B a Q q q a/2 a/2 C Determine an expression for the magnitude and sign of Q so that the net force on the charge at A is zero newtons. A 3 3 Q q 4 B 3 3 Q q 4 C D E 4 3 Q q 3 3 Q q 4 3 4 3 Q q 3 12 27. An electron, initially at rest is accelerated through a potential difference of 550 V. What is the speed of the electron due to this potential difference? A B C D E 28. 106 106 106 106 106 m/s m/s m/s m/s m/s double. quadruple. be cut in half. be cut in fourth. not change. The length of a certain wire is doubled and at the same time its radius is tripled. What is the change in the resistance of this wire? A B C D E 30. × × × × × A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q. If the separation between the plates is doubled, the potential difference between the plates will A B C D E 29. 1.44 1.59 6.10 18.7 13.9 It It It It It stays the same. is reduced by a factor of 4.5. is doubled. is tripled. is quadrupled. A number of resistors are connected across points A and B as shown. What is the equivalent resistance between points A and B? A B C D E 4Ω 6Ω 8Ω 10 Ω 12 Ω 13 31. Five resistors are connected as shown. The potential difference between points A and B is 25 V. 3.6 3.5 A 1.8 2.4 5.1 B How much energy is dissipated in the 1.8-Ω resistor in 4.0 seconds? A B C D E 32. 18 28 55 64 93 J J J J J A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E. It is placed in a uniform magnetic field of 0.85 T in the same plane, directed as shown. What is the magnitude and direction of the force acting on section DE of this wire? A B C D E 0.30 0.12 0.30 0.12 0.20 N N N N N perpendicular perpendicular perpendicular perpendicular perpendicular out of the page into the page into the page out of the page out of the page 14 33. Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. At what point between the two wires are the contributions from the two wires the same? A B C D E 34. A proton, moving west, enters a magnetic field of a certain strength. Because of this magnetic field the proton curves upward. What is the direction of this magnetic field? A B C D E 35. 0.040 m from the 20 A wire 0.080 m from the 20 A wire 0.12 m from the 20 A wire 0.16 m from the 20 A wire 0.18 m from the 20 A wire towards the towards the towards the towards the downward west east south north A conducting rod with a length of 27.0 cm is placed on a U-shaped metal wire that includes a light bulb with a resistance of 60.0 Ω as shown. A constant magnetic field with a strength of 0.600 T is applied perpendicular into the paper. An applied force moves the rod to the right with a constant speed of 6.00 m/s. What is the power consumed by the light bulb? A B C D E 4.00 15.7 11.6 7.57 25.4 mW mW mW mW mW 15 36. The magnetic field and the number of turns of a coil of wire are doubled, while its area is reduced by a factor of 2. Assuming that all the other parameters remain the same, what happens to the induced emf in that coil of wire? A B C D E 37. is doubled. is reduced by a factor of 2. is quadrupled. is reduced by a factor of 4. stays the same. The graph below shows the voltage across and the current through a single circuit element connected to an ac generator. What is the reactance of this element? A B C D E 38. It It It It It 20 25 30 35 40 The figure below shows a simple ac circuit consisting of an inductor connected across the terminals of an ac generator. If the frequency of the ac generator is decreased by a factor of four, what will happen to the inductive reactance on the inductor? A B C D E It It It It It decreases by a factor of 4. decreases by a factor of 8. increases by a factor of 2. increases by a factor of 4. increases by a factor of 8. 16 39. A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the lowest frequency associated with this portion of the spectrum? A B C D E 40. 1.50 7.50 7.50 7.50 1.50 × × × × × 1014 1013 1014 1015 1015 Hz Hz Hz Hz Hz The figure shows the path of a ray of light as it travels through air and crosses a boundary into water. The index of refraction of water for this light is 1.33. 60° air 30° water What is the angle of refraction for this situation? A B C D E 41. 0.37° 0.65° 22° 41° 60° A ray of light is normally incident on face ab of a plastic prism with an index of refraction n = 1.20 as shown below. a incident ray b c Determine the largest value of the angle so that the ray is totally reflected at the face ac if the prism is immersed in air. A B C D E 21° 34° 69° 78° Total internal reflection will not occur for any value of . 17 42. The figure is a scaled diagram of an object and a converging lens surrounded by air. Only one focal point, F, of the lens is shown. The index of refraction of this lens is 1.51 for red light and 1.53 for blue light. Blue light is focused at the point F. Which one of the following statements is true concerning the focal point for red light? A B C D E 43. is is is is is also at F. very close to D. very close to the lens. to the left of and close to F. to the right of and close to F. If the wavelength of light in Young's two-slit experiment is decreased, which one of the following statements is true of the interference pattern? A B C D E 44. It It It It It The distance between the minima stays the same. The distance between the maxima decreases. The distance between the maxima stays the same. The distance between the maxima increases. Impossible to tell without knowing the wavelength of light in use. In a single slit diffraction experiment, the width of the slit is 3.1 × 10 -5 m and the distance from the slit to the screen is 2.2 m. If the beam of light of wavelength 600 nm passes through the slit and forms a diffraction pattern on the screen, what is the linear distance on the screen from the center of the diffraction pattern to the first dark fringe? A B C D E 2.1 4.3 6.3 7.4 8.5 cm cm cm cm cm 18 45. A monochromatic beam of light of wavelength 600 nm is incident normally on a diffraction grating with a slit spacing of 1.70 × 10-4 cm. What is the angle for the first order maximum? A B C D E 46. A 60-W bulb is operating at an efficiency of 6.20%. What is the number of photons per second given off by the bulb assuming the wavelength of light to be 580 nm? A B C D E 47. 5.42 10.8 16.2 21.7 25.3 × × × × × 1018 1018 1018 1018 1018 photons/s photons/s photons/s photons/s photons/s When you decrease, by a factor of two, the wavelength of the light causing photoelectrons to be emitted from a metal surface, the kinetic energy of the photoelectrons will A B C D E 48. 10.5° 12.1° 16.4° 18.2° 20.7° decrease by a factor of 2. double more than double. increase by a factor of √2. decrease by a factor of √2. An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength? A B C D E 409 302 205 420 502 nm nm nm nm nm 19 49. What is the wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from n = 2 state to the ground state? A B C D E 50. 121.5 203.1 243.0 388.8 411.1 nm nm nm nm nm Fermium-253 has a half-life of 3.00 days. A sample of fermium has 7.37 × 107 nuclei. How long will it take for there to be only 3.36 × 106 fermium nuclei in this sample? A B C D E 2.75 9.80 13.4 15.7 58.6 days days days days days END OF PAPER 20