Grade: 11 International Pysics Olympiad Qualifier Set: 2 --------------------------------------------------------------------------------------------------------------- Max Marks: 60 Test ID: 12111 Time Allotted : 40 Mins --------------------------------------------------------------------------------------------------------------- Instructions: Eac question as four coices (A), (B), (C) and (D) out of wic ONLY ONE is correct. Eac question carries 2 Marks. Tere is no negative marking 1. An object moves in two dimensions according to r (t) = (4.0t 2 9.0)î + (2.0t 5.0) ĵ, were r is in meters and t in seconds. Wen does te object cross te x-axis? A. 0.2 s B. 0.4 s C. 0.6 s D. 2.5 s 2. Te grap sows velocity as a function of time for a car. Wat was te acceleration at time = 90 seconds? A. 0.22 m/s 2 B. 0.33 m/s 2 C. 0.44 m/s 2 D. 9.8 m/s 2 3. Te cemical potential energy stored in a battery is converted into kinetic energy in a toy car tat increases its speed first from 0 mp to 2 mp and ten from 2 mp up to 4 mp. Ignore te energy transferred to termal energy due to friction and air resistance. Compared to te energy required to go from 0 to 2 mp, te energy required to go from 2 to 4 mp is A. alf te amount. B. te same amount. C. twice te amount. D. tree times te amount. Page 1 of 9
4. Two weels wit fixed ubs, eac aving a mass of 1 kg, start from rest, and forces are applied as sown. Assume te ubs and spokes are massless, so tat te rotational inertia is I = mr 2. In order to impart identical angular accelerations about teir respective ubs, ow large must F2 be? A. 0.25 N B. 0.5 N C. 1 N D. 2 N 5. A uniform disk, a tin oop, and a uniform spere, all wit te same mass and same outer radius, are eac free to rotate about a fixed axis troug its center. Assume te oop is connected to te rotation axis by ligt spokes. Wit te objects starting from rest, identical forces are simultaneously applied to te rims, as sown. Rank te objects according to teir kinetic energies after a given time t, from least to greatest. (a) disk, oop, spere (b) spere, disk, oop (c) oop, spere, disk (d) oop, disk, spere 6. A non-hookian spring as force F = kx 2 were k is te spring constant and x is te displacement from its unstretced position. For te system sown of a mass m connected to an unstretced spring initially at rest, ow far does te spring extend before te system momentarily comes to rest? Assume tat all surfaces are frictionless and tat te pulley is frictionless as well. A. ( 3mg 1 ) 2 2k B. ( 2mg k ) 1 2 C. ( mg k ) 1 2 1 3 mg D. ( ) 2 2k Page 2 of 9
7. If a planet of radi R spins wit an angular velocity ω about an axis troug te Nort Pole, wat is te ratio of te normal force experienced by a person at te equator to tat experienced by a person at te Nort Pole? Assume a constant gravitational field g and tat bot people are stationary relative to te planet and are at sea level A. g/ Rω 2 B. Rω 2 /g C. 1 Rω 2 /g D. 1+ g/rω 2 8. A ball of mass m is launced into te air. Ignore air resistance, but assume tat tere is a wind tat exerts a constant force Fo in te x direction. In terms of F0 and te acceleration due to gravity g, at wat angle above te positive x-axis must te ball be launced in order to come back to te point from wic it was launced? A. tan 1 (F0 /mg) B. tan 1 (mg / F0) C. sin 1 (F0 /mg) D. te angle depends on te launc speed 9. Find te period of small oscillations of a water pogo, wic is a stick of mass m in te sape of a box (a rectangular parallelopiped.) Te stick as a lengt L, a widt w and a eigt and is bobbing up and down in water of density ρ. Assume tat te water pogo is oriented suc tat te lengt L and widt w are orizontal at all times. Hint:Te buoyant force on an object is given by F = ρ Vg, were V is te volume of te medium displaced by te object and ρ is te density of te medium. Assume tat at equilibrium, te pogo is floating. A. 2π L g B. π ρω2 L 2 g m 2 C. 2π m2 ρω 2 L 2 g D. 2π m ρω L g Instructions for Questions 10 to 12 A simplified model of a bicycle of mass M as two tires tat eac comes into contact wit te ground at a point. Te weelbase of tis bicycle (te distance between te points of contact wit te ground) is w, and te center of mass of te bicycle is located midway between te tires and a eigt above te ground. Te bicycle is moving to te rigt, but slowing down at a constant rate. Te acceleration as a magnitude a. Air resistance may be ignored. Page 3 of 9
Case 1 (For Questions 10-11): Assume tat te coefficient of sliding friction between eac tire and te ground is μ, and tat bot tires are skidding i.e. sliding witout rotating. Express your answers in terms of w,, M, and g. 10. Wat is te maximum value of μ so tat bot tires remain in contact wit te ground? A. ω 2 B. 2ω C. 2 ω D. ω 11. Wat is te maximum value of a so tat bot tires remain in contact wit te ground? A. ωg B. ωg 2 C. g D. 2ω 2ωg Case 2 (For Question 12): Assume, instead, tat te coefficient of sliding friction between eac tire and te ground is different: μ1 for te front tire and μ2 for te rear tire. Let μ1 = 2μ2 12. Assume tat bot tires are skidding: sliding witout rotating. Wat is te maximum value of a so tat bot tires remain in contact wit te ground? A. ωg B. ωg 3 C. 2ωg D. 3 ωg Page 4 of 9
Instructions for Questions 13 to 15 A simple gun can be made from a uniform cylinder of lengt L0 and inside radius rc. One end of te cylinder is sealed wit a moveable plunger and te oter end is plugged wit a cylindrical cork bullet. Te bullet is eld in place by friction wit te walls of te cylinder. Te pressure outside te cylinder is atmosperic pressure, P0. Te bullet will just start to slide out of te cylinder if te pressure inside te cylinder exceeds Pcr. Tere are two ways to launc te bullet: eiter by eating te gas inside te cylinder and keeping te plunger fixed, or by suddenly pusing te plunger into te cylinder. In eiter case, assume tat an ideal monatomic gas is inside te cylinder, and tat originally te gas is at temperature T0, te pressure inside te cylinder is P0, and te lengt of te cylinder is L0. 13. Assume tat we launc te bullet by eating te gas witout moving te plunger. Find te minimum temperature of te gas necessary to launc te bullet. Express your answer in terms of any or all of te variables: P0,T0, Pcr, L0 and rc A. T = ( P o ) L o B. T = ( P o ) T o C. T = ( r c ) T o D. T = ( P 0 ) T o 14. Assume, instead tat we launc te bullet by pusing in te plunger, and tat we do so quickly enoug so tat no eat is transferred into or out of te gas. Find te lengt of te gas column inside te cylinder wen te bullet just starts to move. Express your answer in terms of any or all of te variables: P0,T0, Pcr, L0 and rc A. L = L 0 ( P 0 ) B. L = L 0 ( P 0 ) 2 3 C. L = L 0 ( P 5 0 3 ) D. L = L 0 ( P 7 0 3 ) 15. It is necessary to squeeze te bullet to get it into te cylinder in te first place. Te bullet normally as a radius rb tat is sligtly larger tan te inside radius of te cylinder; rb ra = Δr, is small compared to rc. Te bullet as a lengt << L Te walls of te cylinder apply a pressure to te cork bullet. Wen a pressure P is applied to te bullet along a given direction, te bullet s dimensions in tat x direction cange by for a constant E known as Young s modulus. You may x = P Y assume tat compression along one direction does not cause expansion in any oter direction. (Tis is true if te so-called Poisson ratio is close to zero, wic is te case for cork.) Page 5 of 9
If te coefficient of static friction between te cork and te cylinder is μ, find an expression for Pcr. Express your answer in terms of any or all of te variables P0,T0, Pcr, L0, m, Δr, and rc A. = P o + ( 2E r c 2 ) r B. = P o + ( μe r c 2 ) r C. = P o + ( 2μE ) r r c D. = P o + ( 2Eµ r2 ) r c Instructions for Questions 16 to 19 A certain mecanical oscillator can be modeled as an ideal massless spring connected to a moveable plate on an incline. Te spring as spring constant k, te plate as mass m, and te incline makes an angle θ wit te orizontal. Wen te system is operating correctly, te plate oscillates between points A and B in te figure, located a distance L apart. Wen te plate reaces point A it as zero kinetic energy, but ten trips a small lever tat instantaneously loads a block of mass M onto te plate. Te block and plate ten move down te incline to point B, were te force from te spring stops te plate. At tis point, te block falls troug a ole in te incline, allowing te plate to move back up under te force of te spring. Upon returning to point A it collects anoter block, and te cycle repeats. Bot te plate and te block ave a coefficient of friction μ wit te incline for bot kinetic and static friction. It is reasonable tat te motion in eiter direction is simple armonic in nature. 16. Let μc be te critical value of te coefficient of friction were te block will just start to slide under te force of gravity on an incline (witout te spring acting on it). Let μ = μc/2. Find μ in terms of g, te acceleration of free fall, and any or all of te following variables: θ and M. tan θ A. μ = 2 B. μ = tan θ C. μ = tan 2θ D. μ = tan2 θ 2 17. In order for tis system to work correctly, it is necessary to ave te correct ratio Page 6 of 9
between te mass of te block and te mass of te plate. Tese masses are cosen so tat te downward moving block and plate just stop at point B wile te upward moving plate just stops at point A. Find te ratio R = M/m. A. 1 B. 2 C. 3 D. 4 18. Te system delivers blocks to point B wit period T0, until te blocks run out. After tat, te plate alone oscillates wit a period T. Find te ratio T0/T A. 1+ 3 2 B. 1+ 3 3 C. 1+ 3 4 D. 1+ 3 6 19. Te plate only oscillates a few times after delivering te last block. At wat distance up te incline, measured from point B, does te plate come to a permanent stop? Te stopping points are located at(for integer n.) A. n(mg sin θ )/k and L n(2mg sin θ)/k B. n(2mg sin θ)/k and L n(mg sin θ)/k C. n(2mg sin θ)/k and L n(2mg sin θ)/k D. n(mg sin θ )/k and L n(mg sin θ)/k 20. Te Doppler Effect causes a cange in perception of te pitc of source of sound because in te same period of time A. if te distance between source and observer increases, te waves must spread out B. if te distance between source and observer decreases, te waves must be compressed C. te same number of waves must fit between te source and te observer D. All of te above are correct. 21. An engineer is designing an instrument to examine te interior of a piece of wood witout cutting it. Te engineer decides to pass electromagnetic radiation troug te wood to a detector on te oter side. Wic type of electromagnetic radiation would be most suitable for tis investigation? A. Visible ligt B. Radio waves C. X-rays D. Ultraviolet ligt 22. A mass is connected to an ideal spring, as sown below. As te amplitude increases, te period of te simple armonic motion Page 7 of 9
A. increases. B. decreases. C. some times increases and some time decreases, depending on te friction between te mass and te table. D. stays te same. 23. According to Kinetic Molecular Teory, gas pressure is due to A. te mass of particles. B. te collisions of particles on te walls of a container. C. te forces of repulsion between te particles. D. te energy loss experienced by eac particle. 24. Te Second Law of Termodynamics states tat te of an isolated system never decreases. A. temperature B. volume C. eat energy D. entropy 25. A liquid wit a low viscosity A. as a definite sape B. flows quickly C. flows slowly D. fills its container 26. Wic of te following terms explains wy a liquid will move up a column in capillary tube wit small radius? A. repulsion B. dispersion C. capillary action D. viscosity 27. Te type of energy stored wen an object is compressed under pressure is called? A. friction Page 8 of 9
B. seismic C. tectonic D. elastic 28. According to te Kinetic Molecular Teory of gases, collisions between molecules are perfectly. A. regular B. linear C. plastic D. elastic 29. Wic of tese solutes will decrease te surface tension of water? A. Surfactant B. Sugar cane C. Inorganic salts D. Dettol 30. According to Arcimedes principle, te exerted on a body immersed in a fluid, is equal to te weigt of te fluid tat te body displaces. A. vapor pressure B. dynamic pressure C. surface tension D. buoyant force Page 9 of 9