2021 SAJC H3 Physics QP

Class Index Number Name 20S ST. ANDREW’S JUNIOR COLLEGE JC 2 2021 Preliminary Examination PHYSICS 9814/01 Paper 1 17th September 2021 3 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and Civics Group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, 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 The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 30 printed pages including this page.

2 SAJC 2021 Preliminary Examination / 9814 Data speed of light in free space c = 3.00 x 108 m s-1 permeability of free space 0 = 4 x 10-7 H m-1 permittivity of free space 0 = 8.85 x 10-12 F m-1 (1/(36)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 J s unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mp = 1.67 x 10-27 kg molar gas constant R = 8.31 J K-1 mol-1 the Avogadro constant NA = 6.02 x 1023 mol-1 the Boltzmann constant k = 1.38 x 10-23 J K-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2 Formulae uniformly accelerated motion =s 2 2 1 atut + =2v asu 22 + moment of inertia of rod through one end =I 21 3 ML moment of inertia of hollow cylinder through axis =I ( ) 221 122 +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 a gas =W Vp hydrostatic pressure =p gh gravitational potential = r Gm− Kepler’s third law of planetary motion 2 =T 234 a GM temperature T/K = T/C + 273.15 pressure of an ideal gas p =  2 3 1 cV Nm mean translational kinetic energy of an ideal gas molecule =E kT2 3

3 SAJC 2021 Preliminary Examination / 9814 displacement of particle in s.h.m. x = x0 sin  t velocity of particle in s.h.m. v = v0 cos  t = 22 xxo − 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 = r Q o4 electric field strength due to a long straight wire E = 2  or electric field strength due to a large sheet E = 2  o alternating current/voltage x = x0 sin  t magnetic flux density due to a long straight wire B = d o   2 I magnetic flux density due to a flat circular coil B = r No 2 I magnetic flux density due to a long solenoid B = Ino energy in an inductor =U 21 2 LI RL series circuits  = L R RLC series circuits (underdamped)  = 2 2 1 4 R LC L− radioactive decay x = x0 exp(–t) decay constant  = 2 1 2ln t Section A

4 SAJC 2021 Preliminary Examination / 9814 Answer all questions in this section You are advised to spend about 1 hour 50 minutes on this section. 1 An alpha particle of mass 4 u moving with a velocity 2000 ms-1 collides elastically with a carbon atom of mass 12 u at rest. The alpha particle is scattered through an angle of 30 ° from the original direction. (a) Calculate the magnitude of the velocity of the centre of mass of the 2 particles before the collision. velocity = _______________ m s-1 [1] (b) Construct a vector diagram relating the velocity of the alpha particle in the centre of mass frame and the laboratory frame after the collision. Calculate the magnitude of the velocities of the alpha particle after the collision in the centre of mass reference frame, and the lab frame. velocity in lab frame = ____________ m s-1 velocity in centre of mass frame = ____________ m s-1 [4]

5 SAJC 2021 Preliminary Examination / 9814 (c) Hence determine the velocities of the carbon atom after the collision in the centre of mass reference frame and the laboratory frame, and the velocity direction in the laboratory frame. direction in the lab frame = _________________o velocity in lab frame = _____________ m s-1 velocity in centre of mass frame = _____________ m s-1 [3] [Total: 8] 2 Consider a circular sheet of radius 2R having a uniform density. A circular hole of radius R is made at a distance R from the center of the first circle, as shown in Fig. 2.1. Fig. 2.1

6 SAJC 2021 Preliminary Examination / 9814 (a) Determine the position of the centre of mass of the circular sheet. [2] (b) The centre of mass of the circular sheet is projected with a speed of 22.6 ms-1 at an angle of 45° from the horizontal while rotating forward with an angular velocity of 5π rad s-1 about a horizontal axis passing through the centre of mass. The value of R is 0.600 m. (i) Sketch a path showing how the outer most edge of the hole moves until it hits the ground. [3]

7 SAJC 2021 Preliminary Examination / 9814 (ii) Calculate the number of times the outer most edge of the hole moves backwards horizontally before the disc reaches the highest point of its path. number of times = _____________ [4] (iii) Calculate the vertical velocity of the outermost edge of the hole when its horizontal velocity is zero for the first time. vertical velocity = _____________ m s-1 [1] [Total: 10]

8 SAJC 2021 Preliminary Examination / 9814 3 A spacecraft in low Earth orbit has to be put into an orbit around Venus using Hofmann transfer orbit. The Earth and Venus are in coplanar circular orbit with the Sun as the centre of the circle. Use the data provided below to answer parts (a) and (b). 1 AU = 1.496x 1011m Planets Distance from the Sun / AU Period / s Earth 1.000 3.156 x 107 Venus 0.7233 1.941 x 107 (a) Calculate the change in magnitude of velocity required at the start of the Hofmann transfer and at the destination orbit. change in speed at the start = ___________ m s-1 change in speed at the destination orbit = ___________ m s-1 [4]

9 SAJC 2021 Preliminary Examination / 9814 (b) Calculate the time taken to complete the transfer. time = ____________ days [1] (c) Calculate the angle between Venus and Earth at the start of the transfer. angle between Earth and Venus = ___________ o [2] [Total: 7]

10 SAJC 2021 Preliminary Examination / 9814 4 The circuit in Fig. 4.1 shows a capacitor of capacitance C connected to a switch S that can swing to the left or to the right to make a contact. Switch is initially open. The emf of the source is E and the resistance connected to it is R. The variable resistor R2 is initially set to zero. Each inductor has an inductance