RI 2024 H2 Physics Promo Sect B QP

Name: ( ) CT Group: 25S0 RAFFLES INSTITUTION 2024 YEAR 5 PROMOTION EXAMINATION H2 PHYSICS 9749 2 h 30 min Section B RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Name, Index Number and CT Group 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 a 2B pencil for any diagrams or graphs. The use of an approved scientific calculator is expected, where appropriate. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A / 15 16 / 8 17 / 9 18 / 8 19 / 10 20 / 9 21 / 17 22 / 19 Deductions Total / 95 There are 12 printed pages, inclusive of the cover page, in this booklet.

2 © Raffles Institution 16 To determine the Young modulus E of a metal, a student conducts an experiment on a wire made of the metal. Data collected from the experiment are shown below: ( ) ( ) ( ) ( ) 10.0 0.1 N 0.500 0.001 m 0.5 0.1 mm 0.21 0.01 mm F L d e = ± = ± = ± = ± where F is the applied force L is the original length of the wire d is the diameter of the wire e is the extension of the wire. The Young modulus E is given by the equation: FLE Ae= where A is the cross-sectional area of the wire. (a) (i) Show that the unit of E is equivalent to Pa. [1] (ii) Determine the Young modulus E of this wire, to three significant figures. E = Pa [2]

3 © Raffles Institution [Turn over (iii) Use your answer in (a)(ii) to determine the actual uncertainty in the value of E. Hence give a statement of E , with its uncertainty, to an appropriate number of significant figures. E = ± Pa [3] (b) State the quantity that contributes most significantly to the uncertainty in E and suggest an improvement that can be made to reduce the uncertainty in E. [2] [Total: 8]

4 © Raffles Institution 17 During a basketball game, a player tries to shoot the ball into the hoop when he is 4.0 m away from the hoop. The hoop is 3.0 m above the ground. The ball leaves the player’s hands at a height of 2.0 m above the ground and at angle of 60° from the horizontal and enters the centre of the hoop as shown in Fig. 17.1. Fig. 17.1 (not to scale) Determine: (a) the initial velocity of the ball initial velocity = m s−1 [3] 2.0 m initial velocity 60° 1.0 m 4.0 m ground hoop

5 © Raffles Institution [Turn over (b) the time taken for the ball to move from the player to the hoop time taken = s [1] (c) the maximum height above the ground reached by the ball maximum height = m [3] (d) the magnitude of the change in velocity of the ball from the moment it leaves the player’s hand to the moment it enters the hoop. magnitude of change in velocity = m s−1 [2] [Total: 9]

6 © Raffles Institution 18 Fig. 18.1 shows a swing ride carousel. The seats are suspended using light cables of length L from the circular top of diameter 14 m. When the period of rotation of the top is 8.7 s, the empty seats swing outwards, and the cables are inclined at an angle of 26° to the vertical. (a) Explain why the cables are inclined at an angle to the vertical when the top of the ride is rotating. [3] (b) Show that the angular velocity of the top is 0.72 rad s−1. [1] 14 m L circular top 26° seat Fig. 18.1 (not to scale)

7 © Raffles Institution [Turn over (c) Determine L. L = m [3] (d) A seat is occupied by a child of mass 30 kg and the top rotates with the same angular velocity in (a). State and explain whether the angle at which the cable inclines to the vertical increases, decreases or remains the same at 26°. [1] [Total: 8]

8 © Raffles Institution 19 (a) A planet of mass m is in a circular orbit of radius r around a star of mass M, as shown in Fig. 19.1. Fig. 19.1 The planet and the star may be considered to be point masses at their centres. The planet has an orbital period T. Show that T and r are related by the equation: 2 23 4Tr GM π= where G is the gravitational constant. [2] planet star mass m mass M r

9 © Raffles Institution [Turn over (b) The star ρ−Cancri A has a planetary system like that of the Sun. It has five planets and data for these planets are given in Table 19.1. Table 19.1 planet orbital period / Earth days radius of orbit / m ρ−Cancri A b 14.7 ρ−Cancri A c 44.4 ρ−Cancri A d 5480 8.83 × 1011 ρ−Cancri A e 2.80 5.69 ×109 ρ−Cancri A f 261 (i) Use the equation in (a) and data from Table 19.1 to place the planets in order of orbital distance from ρ−Cancri A. nearest to ρ−Cancri A ρ−Cancri A ρ−Cancri A ρ−Cancri A ρ−Cancri A furthest from ρ−Cancri A ρ−Cancri A [1] (ii) Use data from Table 19.1 for the planet ρ−Cancri A d and the planet ρ−Cancri A e to calculate an average value of the mass of the star ρ−Cancri A. mass of star ρ−Cancri A = kg [3]

10 © Raffles Institution (c) The masses and radii of ρ−Cancri A and the Sun are related by the equations: 5mass of the star ancri A mass of t C he Sun 0.90ρ − = 3radius of the star Cancri A radius of t 9he Sun 0. 4ρ − = . (i) Determine the ratio of the gravitational field strength on the surface of the star ρ−Cancri A to that on the surface of the Sun. ratio = [2] (ii) Use your answer in (b)(ii) to determine the orbital radius of the Earth around the Sun. orbital radius = m [2] [Total: 10]