For candidates applying to Physics, Physics and Philosophy ...

1 1 Physics ADMISSIONS TESTT hursday , 5thof November 2020 Time allowed: 2 hoursFor candidates applying to Physics , Physics and Philosophy ,Engineering, or Materials ScienceTotal 26 questions [100 Marks]Answers should be written on the question sheet in the spaces provided,and you are encouraged to show your should attempt as many questions as you tables, or formula sheets may be should be given exactly and in simplest termsunless indicated multiple-choice answers by circling the best credit may be given for correct workings in multiple choice numbers in the margin indicate the marks expected to be assignedto each question.

2 You are advised to divide your time according tothe marks may take the gravitational field strengthon the surface of Earth to beg 10 m s 2Do NOT turn over until told that you may do page is left intentionally stable isotopes of carbon, nitrogen and oxygen are represented symbolicallybelow:126C ,136C ,147N ,157N ,168O ,178O ,188 OWhich of the following statements are true?[2] has a larger number of protons has a larger mass has a larger nuclear charge has a larger mass per unit charge has a larger number of neutrons , 3, 43, 4, 52, 3, 41, 2, 32, 3, triangleABChas vertices at points in two-dimensional Cartesian co-ordinatesA: (0,1),B: (1,2), andC: ( 1,2).

3 It is reflected in the liney=xand then rotatedaround the origin by 90 degrees in a clockwise direction. Which single transformationmaps the initial triangle to the final state of the above transformations?[2]ABCDE reflection inx= 0reflection iny= 0rotation by 180 anti-clockwisearound the originrotation by 90 anti-clockwisearound (2,0)scale factorof ammeter A, B, C, D, E gives the highest reading?[2]RR2 log2x+ log2(2x+ 3) = 1 forx.[2]ABCDEx= 2x=12x= 1x= 2 and12x= the gravitational field strength at the Earth s surface isgE= 10 N/kg, and ata distanceR > REfrom its centre the field strength isgR= 2 N/kg, what is the radiusof the EarthREin terms ofR?

4 [2]ABCDER/25R/5R/ 10R/ 5R/ the functiony(x) = sin(100x). The angle is in degrees, so that sin(180) =0. How many maxima ofy(x) occur forx > [2]ABCDE01314 is the order, from shortest to longest, of the wavelengths of the peak elec-tromagnetic emission from each of the following objects?[2]1. an electric torch2. a microwave oven3. a radioactive source4. a hot cooking stove5. a short-wave radio particle of type X decays with equal probability either to a pair of particles oftype Y or a pair of particles of type Z. Both Y and Z particles are decays of two X particles are observed. A pair of Y particles is found amongthe decay products.

5 What is the probability that a pair of Z particles is among thesedecay products?[2]ABCDE1/41/31/22 students need to complete their compulsory practicals for their high schoolexaminations as detailed in the table below:No. of studentsNo. of different practicals to complete214243 The school only has one laboratory in which several different experiments can be setup simultaneously. A maximum of six students are allowed in the school s laboratoryfor a lesson. Each practical takes one lesson. What is the minimum number of lessonsrequired to complete all the practicals?[2] is the next number in the sequence?

6 37, 41, 43, 47, 53, 59[2] stone of average diameter 10 cm is hit with a hammer and splits into time the stone or one of its pieces is hit, it splits into three further pieces of equalvolume and similar shape. How many hits will it take before a piece reaches the size ofa typical atom?[2] graph below shows a functionf(x).b2bxIfais a constant such that 0< a < b, identify the sketch ofg(x) = f(a x)from the sketches below.[2] a set of masses of three different valuesma,mbandmc. Each of thefollowing three combinations have the same total two masses ofmaplus three masses ofmb2. five masses ofmaplus one mass ofmc3.

7 Two masses ofmaplus one mass ofmbplus one mass ofmcFindmbandmcin terms ofma.[4] all solutions of the following equation in the range 0 360 .4 cos2( ) + 2( 3 1) sin( ) = 4 3[3] >h0mx0v0h0 LThe above figure depicts a ball of massmwhich is equipped on its lower sidewith a massless spring of uncompressed lengthL0and spring constantk. The spring isinitially compressed to a lengthL < L0, as shown in the ball-spring system is either dropped vertically or launched with a horizontal speedv0from a height ofh0at a distancex0from a wall of spring remains compressed until it touches the ground. When it touches the groundthe spring is released (by a mechanism not shown on the figure) and expands very quicklyback to its uncompressed lengthL0and is then held fixed at bounce of the ball-spring system on the ground is assumed to be totally elastic.

8 (a) When the ball is dropped vertically, find the maximum heighthmaxthe ball-spring system could reach after its bounce in terms of the spring s compression L=L0 L, and the parametersm,g,kandh0. In analogy toh0in the figure,hmaxshould be the vertical distance between the floor and the lower endof thespring afterthe bounce. You may takeg= 10 m s 1.[3](b) Find the optimal value for the distancex0from which the ball would bounce overa wall with maximum value ofhW.[6]18 This page intentionally left blank for page intentionally left blank for thatdf(x)dx= 2x x12+13dg(x)dx=f(x)determineg(x) such thatf(1) = 1 andg(1) = 0.

9 [4] indicated in the figure, a motor bike of total massm(mis the mass of bike plusrider) is ridden along a horizontal trajectory of radiusRon the inside of a cylindricalcage .R biketrajectoryThe bike and the rider are inclined at an angle to the wall. The angles thatthe bike can make with respect to the walls of the cage are limited by its handle barsto a certain minimum min>0. The tyres of the bike have a very high co-efficient offriction with the cage so that the tyres can only roll but not slip along the cage.(a) Show in a diagram the forces acting on the bike if it is to maintain a horizontaltrajectory as shown in the figure.

10 [2](b) At what minimum speedvminmust the bike travel if it is not to fall down?[3](c) Given that min= 30 ,R= 4 m,g= 10 m s 2,m= 250 kg find a numerical valueforvmin.[1]22 This page intentionally left blank for whichxis the following inequality satisfied?2x2+ 3x 22x2 3x 2>0[6] Euler numberEuhas no units. It is used in fluid flow calculations. It dependson the pressureP, density , and fluid velocityvsuch that:Eu=Pa bvcwherea,bandcare the ratio ofa:b:cin its simplest form, wherea,bandcare positive or negativeintegers.[4] the coordinates of the point(s) at which the liney=m(3x 2) is tangentto the curvey= 9x2+ 6x 7.