NANYANG TECHNOLOGICAL UNIVERSITY SINGAPORENANYANG TECHNOLOGICAL UNIVERSITY SINGAPORE ENTRANCE EXAMINATION NTUP1 – PHYSICS (Sample) Time Allowed : 2 hours INSTRUCTIONS 1. 2. This paper consists of THREE (3) Sections and comprises NINE (9) pages. Answer ALL the questions in Section A (10 questions) and Section B (3 questions). For Section C, answer ANY TWO (2) questions. For Section A, each multiple choice question carries 2 marks. For Section B, the marks are allocated at the end of each question. For Section C, the marks are allocated at the end of each part of the question. Answers for Section A must be submitted on the answer sheet provided. Answers will be graded for content and appropriate presentation. 3. 4. 5. 6. A list of physical constants is provided on page 9. ________________________________________________________________________________ SECTION A COMPULSORY This Section consists of TEN (10) multiple choice questions. Choose the correct answer from the alternatives given. In your ANSWER SHEET, shade the correct letter (A), (B), (C), or (D) next to the question number. Each question carries two marks. 1. A bullet of mass m = 0.01 kg is fired into a ballistic pendulum of mass M = 2.0 kg as shown in Figure 1. The bullet remains in the block after the collision and the whole system rises to a maximum height of h = 8 cm. What is the bullet’s initial speed? A. B. C. D. 18 m s-1 80 m s-1 150 m s-1 250 m s-1 m M h Figure 1 1 2. Two rods of equal lengths and crosssectional areas but of different materials are placed in thermal contact as shown in Figure 2. The thermal conductivity of Q 0o C P Q 100 o C Figure 2 is half that of P. The outer end of P is at 0o C and that of Q is at 100°C. What is the temperature of the interface at steady state? A B C D 3. 23.88o C 33.33°C 66.66o C 80.39o C A 40 g ice cube at 0°C is added to 200 g of water at 20°C. Calculate the final equilibrium temperature, assuming no other agents for heat exchange are present. The specific heat of ice is 2310 J kg-1 °C-1, and that of water is 4200 J kg-1 °C-1 and the specific latent heat of melting of ice is 3.36 × 105 J kg-1. A. B. C. D. 2.1°C 3.3°C 4.3°C 7.0°C 4. In two experiments with a continuous flow calorimeter to determine the specific heat capacity of a liquid, an input power of 60 W produced a rise of 10 K in the liquid. When the power was doubled, the same temperature rise was achieved by making the rate of flow of liquid three times faster. The power lost to the surroundings in each case was A. B. C. D. 20 W 30 W 40 W 120 W 5. Double-slit interference is investigated using light of wavelength 600 nm. The fringe spacing is 1.44 mm. If the screen is 1.2 m away from the slits, how far apart are the slits? A. B. C. D. 2.5 mm 0.50 mm 0.25 mm 0.050 mm 2 6. A loudspeaker which emits sound of frequency 1000 Hz is placed several metres from a plane reflecting wall in a large chamber containing a gas. A microphone M, connected to a cathode ray oscilloscope, detects a series of low and high intensity signals as it moves along the line joining the loudspeaker B and the wall. Figure 3 If the microphone detects a series of 10 low intensity signals while moving through a distance S of 2.0 m, what is the speed of sound in the chamber? A. B. C. D. 110 ms-1 220 ms-1 330 ms-1 440 ms-1 7. A small-amplitude progressive wave in a stretched string has a velocity of 10 m s-1 and a frequency of 100 Hz. What is the phase difference, in radians, between two points 2.5 cm apart in the string? A. B. C. D. π 8 π 4 3π 8 π 2 8. A uniform wire is made of material with resistivity ρ. It has a length of L and its diameter is d. When a constant current I flows through the wire, what is the rate at which heat is generated in the wire? 3 A. B. C. D. 4 IρL πd IρL πd 2 4 I 2 ρL πd 2 2 4 ρL I 2 2 πd 9. In the circuit shown in Figure 4, the power which is dissipated as heat in the 6-Ω resistor is 6 W. Figure 4 What is the value of resistance R in the circuit? A. B. C. D. 6Ω 10 Ω 13 Ω 24 Ω 10. Half lives of two uranium isotopes U238 and U235 are known to be 4.5 × 109 yr and 7.1 × 108 yr, respectively. If the earth was formed with equal amounts of the two isotopes, estimate the current age of the earth given that uranium ores are 99.29% of U238 and 0.71 % of U235 by number. A. B. C. D. 2 × 109 yr 4 × 109 yr 6 × 109 yr 8 × 109 yr 4 SECTION B Answer ALL the questions in this Section. 1. A glass sphere of volume 7 l contains air at 27°C and is connected to a pipe filled with mercury as shown in Figure 5 below. At the start, the mercury meniscus is level with the bottom of the sphere on both arms of the pipe. The air in the sphere is now heated and the mercury level on the right arm rises 5 mm. If the cross sectional area of the pipe is 10 cm2, what is the new temperature of the air (in °C)? [7 marks] sphere mercury Figure 5 2. (a) In practice, the suspension system of a car consists of a spring under compression combined with a shock absorber which damps the vertical oscillations of the car. Draw sketch graphs, one in each case, to illustrate how the vertical height of the car above the road will vary with time after the car has just passed over a hump if the shock absorber is: (i) not functioning. (ii) operating normally. When the driver of mass 80 kg, steps into the car of mass 920 kg, the vertical height of the car above the road decreases by 2.0 cm. If the car is driven over a series of equally spaced humps, the amplitude of the vibration becomes much larger at one particular speed. (i) Explain why this occurs. (ii) Calculate the separation of the humps if it occurs at a speed of 15 ms-1. [12 marks] (b) 5 3. 100A P 100A Q Strings 0.2m R Figure 6 S Figure 6 shows a very long horizontal wire PQ carrying a current of 100 A flowing in the direction from Q to P. A copper wire which has a diameter of 0.4 mm and as long as the wire PQ is suspended horizontally at a distance 0.2 m below the wire PQ by two strings. If the density of copper is 8900 kg/m3, determine the direction and the minimum value of the electric current which must flow in the wire RS so that the tension in the strings become zero. [11 marks] 6 SECTION C Answer ANY TWO questions from this Section. 1. (a) (b) State the first law of thermodynamics. [5 marks] Most gases increase in temperature when compressed. Where does the energy for this come from? Explain in 50 words or less. [5 marks] Explain in 50 words or less why a visible condensation forms when a can of soda is opened. [5 marks] When 5 g of water is boiled at 100 °C and 100 kPa pressure, 8355 cm3 of steam is formed. The specific latent heat of vaporisation of water is 2.26 MJ kg-1. The questions below require you to give the numerical value as well as sign of certain physical quantities. (i) How much work is done by the expanding water vapour? (ii) What heat energy is absorbed by the water while it boils? (iii) What is the increase in the internal energy of the water molecules? [10 marks] What are the conditions that must be satisfied in order that two source interference fringes may be clearly observed? [4 marks] Figure 7 below illustrates a typical set-up of the Young’s Double Slit experiment. (c) (d) 2. (a) (b) Fig. 7 The distance between the double slits to the screen is 3.0 m. The slit separation is 0.2 mm, and the wavelength of incident light is 633 nm. (i) (ii) (iii) (iv) Determine the angular displacement of the third order minima. Determine the fringe width of the interference pattern observed on the screen. Estimate the theoretical maximum number of bright fringes that can be observed. If the widths of the slits are assumed to be infinitely small and y is the distance from the central maxima on the screen, sketch a clearly labelled graph to show the variation of the intensity of the fringe pattern with y. The intensity of the waves from each slit is I0. Express the intensity in terms of I0. 7 (v) The slit S1 is now covered with a filter such that the light emerging from S1 is reduced by half in amplitude. Sketch on the same graph for part (iv), the new intensity pattern you would expect to observe. Label your graphs clearly. [15 marks] (c) In reality, the interference pattern of the above experiment is as shown in Figure 8 Figure 8 Explain the reason for fall out in the intensity of fringes near the edge of the screen. [6 marks] 3. (a) Lanthanum has two isotopes 138 La and 139 La . The half-life of 138 La is 1.1x10 9 years. In a sample containing both isotopes, the concentration of 138 La atoms is 0.1 %. Calculate the rate of decay of 138 La in 1 kg of lanthanum. (Avogadro constant = 6 × 10 23 mole -1). [5 marks] An X-ray tube operated at a DC potential difference of 40 kV, produces heat at a rate of 720 W. Assume that 0.5% of energy of the electron is converted into X-rays. Calculate (i) the number of electrons per second striking the target; (ii) the velocity of the incident electron. The charge-to-mass ratio of the electron, (b) e = 1.8 × 1011 C Kg-1. me [6 marks] (c) When Cesium is illuminated with light of wavelength 546 nm, the maximum speed of the electron emitted is 3.63 x10 5 m/s. What is the maximum speed of the emitted electrons when the metal is illuminated by light of wavelength 450 nm? [7 marks] A hydrogen atom in the n=4 state makes a transition to the ground state, emitting one photon. Calculate the wavelength of the emitted photon and the recoil velocity of the atom. [7 marks] (d) - End of Paper - 8 SOME FUNDAMENTAL CONSTANTS OF PHYSICS Constant Speed of light in vacuum Elementary charge Electron rest mass Permittivity of free space Permeability of free space Proton rest mass Neutron rest mass Planck's constant Universal gas constant Avogadro's number Boltzmann’s constant symbol c e me εo mo mp mn h R N k value 2.998 x 108 m/s 1.602 x 10-19 C 9.109 x 10-31 kg 8.854 x 10-12 F/m 1.257 x 10-6 H/m 1.673 x 10-27 kg 1.675 x 10-27 kg 6.626 x 10-34 Js 8.314 J/mol K 6.022 x 1023 mole-1 1.381 x 10-23 J K-1 9