2021 NYJC 2021 H3 Physics 9814 P1 (no solutions)

NYJC 2021 9814/01/JC2Prelim/21 [Turn over NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 3 CANDIDATE NAME CLASS TUTOR’S NAME CENTRE NUMBER S INDEX NUMBER PHYSICS 9814/01 Paper 1 22 September 2021 3 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and class in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Section A Answer all questions. You are advised to spend about 1 hour and 50 minutes on Section A. Section B Answer two questions only. You are advised to spend about 35 minutes on each question in Section B. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 2 3 4 5 Section B 6 7 8 Total This document consists of 28 printed pages.

2 NYJC 2021 9814/01/JC2Prelim/21 Data speed of light in free space c = 3.00  108 m s−1 permeability of free space o = 4  10−7 H m−1 permittivity of free space 0 = 8.85  10−12 F m−1 = ( )( )1/ 36   10−9 F m−1 elementary charge e = 1.60  10−19 C the Planck constant h = 6.63  10−34 J s unified atomic mass constant u = 1.66  10−27 kg rest mass of electron me = 9.11  10−31 kg rest mass of proton mp = 1.67  10−27 kg molar gas constant R = 8.31 J K−1 mol−1 the Avogadro constant NA = 6.02  1023 mol−1 the Boltzmann constant k = 1.38  10−23 J K−1 gravitational constant G = 6.67  10−11 N m2 kg−2 acceleration of free fall g = 9.81 m s−2 Formulae uniformly accelerated motion s = 21 2ut at+ v2 = u2 + 2as moment of inertia of rod through one end I = 21 3 ML moment of inertia of hollow cylinder through axis I = 22 12 1 ()2 M r r + moment of inertia of solid sphere through centre I = 22 5 MR moment of inertia of hollow sphere through centre I = 22 3 MR work done on/by gas W = pV hydrostatic pressure p = gh gravitational potential  = −Gm/r Kepler’s third law of planetary motion T2 =  234 a GM temperature T/K = T/°C + 273.15

3 NYJC 2021 9814/01/JC2Prelim/21 pressure of an ideal gas p = 21 3 Nm cV  mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = 0 sinxt  velocity of particle in s.h.m. v = 0 cosvt  = ( ) 22 0xx− electric current I = Anvq resistors in series R = R1 + R2 + … resistors in parallel 1/R = 1/R1 + 1/R2 + … capacitors in series 1/C = 1/C1 + 1/C2 + … capacitors in parallel C = C1 + C2 + … energy in a capacitor U = 21 2CV electric potential V = 04 Q r electric field strength due to a long straight wire E = 02 r   electric field strength due to a large sheet E = 02   alternating current/voltage x = 0 sinxt  magnetic flux density due to a long straight wire B = 0 2 d   I magnetic flux density due to a flat circular coil B = 0 2r  NI magnetic flux density due to a long solenoid B = 0 nI energy in an inductor U = 21 2 LI RL series circuit  = L R RLC series circuits (underdamped)  = 2 2 1 4 R LC L − radioactive decay x = 0 tx −e decay constant  = 1 2 ln2 t

4 NYJC 2021 9814/01/JC2Prelim/21 Section A Answer all questions in this section. You are advised to spend about 1 hour 50 minutes on this section. 1 (a) Explain why the center of mass frame of reference is also the zero momentum frame of reference. [1] (b) A ball of mass m to the right with velocity u and make an elastic collision with a stationary ball of mass m2 as shown in Fig 1.1 The two balls is scattered by a certain angle after the collision as shown in Fig. 1.2. The ball with mass m1 is scattered by an angle 1 with a velocity of v1 . u stationary m1 Fig. 1.1 m2 v1 m1 Fig. 1.2 m2 1

5 NYJC 2021 9814/01/JC2Prelim/21 (i) Show the scatter angle 1 of the ball with mass m1 in the laboratory frame of reference is related to the new scatter angle  in the center of mass frame of reference by the following relation 1 sintan cos ' CMv u = +   where u’ is the initial velocity of ball A in the center of mass frame of reference. [5] (ii) If the two balls have equal mass, use the relationship in (b)(i) to determine the value of  when 1 = 45o angle  = [3]

6 NYJC 2021 9814/01/JC2Prelim/21 (iii) Explain why the value  is always less than the value of . [2] [Total: 11]

7 NYJC 2021 9814/01/JC2Prelim/21 2 (a) A solid sphere of radius R and mass M is released from rest at the top of an inclined plane as shown in Fig. 2.1. The inclined make an angle of  with the horizontal. The coefficient of friction is . Assume the sphere rolls down the slope without slipping. (i) Determine the linear acceleration of the sphere in terms g and . linear acceleration = [3] (ii) Determine an expression for the angular acceleration of the sphere. angular acceleration = [2]  Fig. 2.1

8 NYJC 2021 9814/01/JC2Prelim/21 (b) Explain why when the angle of the slope is increased, there is a critical angle which the sphere will roll and slips down the slope if the angle of the slope is more than this value. [2] (c) Determine this critical angle given that the value of coefficient of friction = 0.30. critical angle = [3] [Total: 10]

9 NYJC 2021 9814/01/JC2Prelim/21 3 A plano-cave lens having refractive index of 1.50 is placed on a flat glass plate, as shown in Fig. 3.1. Its curved surface, with radius of curvature 8.0 m, is on the bottom. The lens is illuminated from above with yellow sodium light of wavelength 589 nm, and a series of concentric bright and dark rings is observed by reflection. The interference pattern has a dark spot at the center, surrounded by 50 dark rings, of which the largest is at the outer edge of the lens. (a) By considering the paths of ray 1 and ray 2, explain how the series of bright and dark ring is formed. [2] (b) Explain why there is a phase change of 180o for ray 2 when it is incident on the flat glass plate based on the evidence that the position which the path difference between ray 1 and ray 2 is zero correspond to a dark ring. [2] (c) Determine the thickness of the air layer at the center of the interference pattern. thickness = m [3] ray 1 ray 2 Fig. 3.1 flat glass plate plano-cave lens

10 NYJC 2021 9814/01/JC2Prelim/21 (c) Calculate the radius of the outermost ring. radius = m [2] (d) (i) A second yellow light of wavelength 589.6 nm is used instead. Determine whether the number of dark rings will still be 50. [2] (ii) Suggest why the intensity of the dark ring near the center if higher compared those near the edge. [1] [Total: 12]