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1 SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Annual Exam 2012 Subject: PHYSICS Level: ADVANCED 1 ST Year Time: 3 hrs Name: Year: Answer all questions. This paper carries 200 marks. 1. A student derived this equation for the period of a pendulum T = 4Π l/g, where g is the acceleration due to gravity and l is the length. Using the method of homogeinity of equations, find whether the equation may be correct or not. (3marks) 2. A ball is let to fall to the ground. It then rises up to one quarter of the initial heght. Sketch displacement time graph, velocity tme graph and an acceleration time graph for the motion. Take downward direction to be negative. Assume there is no air resstance. Mark on the velocity time graph the place where it touches the ground, leaves the ground and where it reaches its maximum height after rebound. (7 marks) 3. An optical fibre consists of a core made from glass Y surrounded by a cladding made from a different glass. The table gives the refractive index for light travelling from air to glass for three glasses. Glass X Y Z Refractive Index a) State which of the glasses X or Z is suitable for the cladding, giving a reason for your answer. b) Determine the critical angle for light passing from the core into the cladding. c) What is the advantage of having a big critical angle. (2 x 3 marks) 4. A missile is projected at 45 degrees to the horizontal with a speed of 200 m/s. a) What is the time of flight? b) What is the range of the missile? 1

2 c) What have you assumed? (3+3+1 marks) 5. A friction free trolley of mass 2kg s tethered to rigid supports at each end by two identical springs of spring constant 20 Nm -1 each. The springs obey Hooke s Law and remain in tension as the trolley is displaced 2 cm to one side and released. a) What is the effective spring constant of the system tethering the trolley? b) What is the frequency of the resulting simple harmonic motion? (3+3 marks) 6. In a race, a skier of mass 60 kg is sliding down a slope with a constant velocity of 12 m/s. The only forces opposing his motion are friction and air resistance which are constant, and together are equal to one fourth of her weight. i) Draw a diagram showing all the forces acting on the skier. (3) ii) Determine the angle that the slope makes with the horizontal. (3) iii) After the skier passes over the finishing line, she uses her skiing sticks to come to rest over a distance of 5 m. Find the force done by the skiing sticks to stop her. (3) iv) What is the heat developed while she is braking. (2) 7. Consider a gas enclosed in a cubic box of side L. There are N particles in the gas, each of mass m. Show that the pressure it exerts on the walls of the box is related to its density by P=⅓ρ v 2 where v 2 is the mean square velocity. (8) 8. Describe an experiment to find the specific latent heat of fusion of ice. (10) 9. The ends of a bar of uniform cross-section are maintained at steady different temperatures, both being above room temperature. Explain how the temperature varies along the bar if the bar is a) ideally lagged b) unlagged. A bar 0.2 m in length and of cross-sectional area 2.5 x 10-4 m 2 is ideally lagged. One end is 373 K while the other is maintained at 273 K by immersion in melting ice. Calculate the rate at which the ice melts owing to the flow of heat along the bar. (Thermal Conductivity of the material of the bar = 4.0 x 10 2 Wm -1 K -1. Specific latent heat of fusion of ice = 3.4 x 10 5 Jkg -1.) (2,2,3,3) 2

3 10. A uniform horizontal beam of weight 200 N and length 2.5 m is freely hinged at one end to a wall. A rope is attached to the free end. The other end of the rope is attached to the wall at a point vertically above the beam so that the rope makes an angle of 30 o with the vertical. a) Draw a free body force diagram for the beam. b) Calculate the tension in the rope. c) Calculate the horizontal and vertical resolved parts X and Y of the push of the wall on the beam. d) Show on your diagram the direction of the resultant of X and Y. (10) 11. A 15.0 V battery with terminals A, B and an internal resistance of 1.0 Ω, and a 5.0 V battery with negligible internal resistance are connected in a circuit with four resistors as shown. i) Use Kirchoff s Laws to find the current through each cell. ii) Calculate the terminal potential of the 15.0 V battery, V AB. iii) What is the voltage drop across the 18.0 Ω resistor and what power is dissipated across it? (9 marks) 12. Explain the following observations concerning the photoelectric effect. a) For any metal surface, electrons are only emitted if the frequency of the incident light is above some threshold value. (so weak UV can emit electrons from zinc, while very intense infrared cannot) 3

4 b) The maximum kinetic energy of the ejected electrons depends only on the frequency of the incident radiation. (8 marks) 13. The universe began with a Big Bang a) Give two proofs of the Big Bang. b) State Hubble s Law. c) If Hubble s constant is 70 kms -1 Mpc -1, estimate the age of the Universe. (1 parsec = 3.26 light years. Speed of light = 3 x 10 8 m/s) (2,2,3 marks) 14. A model aeroplane X has a mass of 0.5 kg and has a control wire OX of length 10 m attached to it. The wire OX is inclined at 60 o to the horizontal and fixed to a point O and X takes 2 s to fly once round its circular path. Calculate: a) the tension T in the control wire. b) the upward force on X due to air. (8) 15. A communication satellite revolves around the Earth in a circular orbit in the equatorial plane, at a height of km above the Earth s surface. Find the period of revolution of the satellite and comment on the result. (Mass of Earth = 5.97 x kg ; Radius of Earth = 6.38 x 10 6 m ; Gravitational Constant = 6.67 x Nm 2 kg -2 ) (8) 4

5 16. a) Describe briefly how one may measure the wavelength of a monochromatic light source using a double slit arrangement. Your answer should include: i) a labelled diagram showing the arrangement of the apparatus. ii) approximate values for the main dimensions used. iii) a list of measurements that need to be taken and the means by which each is measured iv) the formula used, including an explanation of the symbols. (3,2,3,2 marks) b) Light from a cadmium discharge lamp can be used to determine the spacing of the lines on a plane diffraction grating. i) The angle at which the first order diffracted beam makes on either side of the normal is 46 o 13. Calculate the number of lines per metre on the grating if the red light in the cadmium spectrum has a wavelength of 644 nm. ii) Explain why a diffraction grating is preferred to a prism in spectrum analysis. (4,2 marks) 17 a) State the second law of thermodynamics as applied to a heat engine, and comment on its impact on the efficiency of the engine. (3, 2) b) An ideal gas undergoes a cycle of changes in the cylinder of a diesel engine. These changes are represented on the graph. i) Name the type of processs taking place along lines B to C and D to A. (2) ii) The temperatures of the gas at A and B are 300 K and 660 K respectively. Find the temperatures at C and D. (2, 2) 5

6 c) During each part of the cycle descrbed in (b), the gas undergoes changes in internal energy. Some of the factors affecting the changes are tabulated below. Part of Cycle Heat Supplied/ joules Work Done / joules A to B B to C C to D D to A i) Explain why some values are positive and some are negative. ii) Find the work done on the gas in part D to A. iii) Calculate the change in internal energy during the each part of the cycle.(2,1,4) d) ) i) What is the value of the total change in the internal energy of the gas during one complete cycle? (1) ii) comment on the answer obtained (1) 18. As an alternative to a petrol engine, a prototype car is fitted with a flywheel. This is spun to a high speed at the start of the journey. To start the car the flywheel is connected to the drive wheels by a system of gears. The rotational energy stored in the flywheel is then used to propel the car. The flywheel has a moment of inertia of 90 kgm 2. Before each journey the flywheel is accelerated until it has an angular speed of 300 rad/s. a) Assuming the angular acceleration to be uniform, determine the torque required to accelerate the flywheel to its maximum speed in 2.5 minutes. b) Calculate the energy stored in the flywheel at the start of the journey. (3+3 marks) 19 a) A coil of 1000 turns and resistance 23 Ω encloses an area of 4.0 cm 2. It is placed with its plane perpendicular to a magnetic field of flux density 6.0 x 10-5 T. i) If the magnetic field is removed steadly in 5.0 x 10-3 s, what is the average induced emf? ii) What average current flows in the coil it its ends are short-circuited? b) Defne self-inductance. c) An electric motor is connected across a 230 V supply. When steady rotation is reached, the current flowing through the 1Ω armature coil is only 10 A. 6

7 i) Explain why the current is low. ii) Find the power dissipated as heat. iii) Calculate the mechanical power developed by the motor. iv) Find the effcency of the motor. ( 3, 2,2, 3,2,4,2) 20. i) The figure shows the trajectories of some alpha particles passing through thin metal foil close to a nucleus, in a Rutherford scattering experiment. Explain how these observations may be used to establish a nuclear model of the atom. ii) A nucleus of nucleon number A has a radius r =(1.2 x ) A ⅓ metres. Assuming that protons and neutrons have the same approximate mass of 1.67 x kg, estimate the density of a nucleus. iii) A 4.0 MeV alpha particle is directed towards a gold nucleus containing 79 protons. Find the distance of closest approach if a head-on collision is involved. iv) Explain how it is possible for a number of protons to stay together in a nucleus in spite of the electrostatic repulsion. b) A uranium nucleus of mass number 238 and atomic number 92 emits an alpha particle and a gamma ray photon. It becomes an isotope of thorium Th. i) Write down the nuclear equation. ii) Find the total energy released in joules. (6.3.5,2, 3,3) Permittivity of free space equals 8.9 x Fm -1. Charge on an electron equals 1.6 x C Mass of a uranium atom equals u. Mass of a thorium atom equals u. Mass of an alpha particle equals 4.004u, 1 u equals 1.66x10-27 kg. Velocity of light equals 3 x10 8 ms -1 ) END OF PAPER

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