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Exam Class 12 2019 : Physics

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Ashish Singh
Bishop Johnson School & College, Allahabad
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FACULTY RECRUITMENT TEST CATEGORY - B INTERNATIONAL OLYMPIAD (PHYSICS) PAPER-B Time: 1 Hour Maximum Marks: 40 Name:................................................................................. Marks: Subject: ........................................... Instructions * Attempt all questions. * Paper 2 has Two Parts I and II. Each question of Part I carries 2 marks and each question of part II caries 5 marks. * Calculators and log tables are not permitted. PART I 1. The period of a particle executing SHM is T. There is a point P, at a distance x from the mean position O . When the particle passes P towards OP, it has speed v. Find the time in which it returns to P again. 2. A rod of mass m and length is lying along the y-axis such that one of its ends is at the origin. Suddenly an impulse is given to the rod such that immediately after the impulse, the end on the origin has a velocity v0 i and the other end has a velocity 2v 0 i . Calculate the magnitude of angular momentum of the rod about the origin at this instant. 3. A conducting square loop of resistance R = 50 of side a = 1 m, with sides parallel to x and y axis is moved with velocity v = 1 m/s in the positive x-direction in a magnetic field along the negative z-direction. The value of magnetic field varies with time as well as along x-direction given by B(x, t) = 100 xt Tesla. The left edge of the loop is at origin at t = 0. Find the value of current induced in the square loop having resistance R = 50 at t = 1 sec in ampere. 4. y a v B a x A thermally insulated vessel contains some water at 0 C. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given Latent heat of vaporization of water at 0 C = 21 105 J/kg and latent heat of freezing of water = 3.36 105 J/kg. Find the maximum percentage amount of water that will be solidified in this manner. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. FACREC- CAT-B(OLY)-P2-PH-2 5. A rod of length 1000 mm and co-efficient of linear expansion = 10 4 / C is placed on a horizontal smooth surface symmetrically between the two fixed walls separated by 1001 mm. The Young s modulus of the rod is 1011 N/m2. If the temperature is increased by 20oC, then find 2 the stress developed in the rod (in N/m ) approximately. 1000 mm 1001 mm 6. An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Find the refractive index of the liquid. 3h h 2h 7. The wavelength K X-rays produced by an X-ray tube is 0.76 . Find the atomic number of anticathode materials. 8. A non conducting infinite rod is placed along the z-axis: the upper half of the rod (lying along z 0) is charged positively with a uniform linear charge density + while the lower half (z < 0) is charged negatively with a uniform linear charge density . The origin is located at the junction of the positive and negative halves of the rod. A uniformly charged annular disc (surface charge density : 0) of inner radius R and outer radius 2R is placed in the x-y plane with its centre at the origin. Find the force on the rod due to the disc. + 0 R 2R 9. In Young s double slit experiment with light of wavelength = 600 nm intensity of central fringe is 0 . Now one of the slit is covered by glass plate of refraction index 1.4 and thickness t = 5 m, find the new intensity at the same point on screen. 10. A belt of mass 2 kg is wrapped over two cylindrical wheels of small radii rolling on a horizontal rough surface. Each wheel has velocity 3 m/s (see in the figure) and assume that the belt does not slip. What will be the kinetic energy of the belt (in joule). Belt 3m/s 3m/s PART II 11. A block B is floating in the river. The position of the block is as shown in figure at time t = 0. Flow speed of river is 2 m/s. A stone is thrown from point O at time t = 0 with a velocity v = (v1 i + v2 j + 20) k m/s. (a) Find v 1, v 2 such that the stone hits the block. y 2 m/s B 40 m O x (b) If the speed of throw is kept fixed, what is the maximum value of time t at which it is possible to throw the stone to hit the block. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. FACREC- CAT-B(OLY)-P2-PH-3 12. In a certain region of gravity free space there exists a uniform and constant electric field of magnitude E along the positive y-axis of a co-ordinate system. A charged particle of mass 'm' and charge ' q' (q > 0) is projected with speed 2v at an angle of 60 with the positive x-axis in x y plane from the origin. 2 When the x-coordinate of the particle becomes 3mv , a uniform and constant magnetic field of qE strength B is also switched on along the positive y-axis. Find the co-ordinate of the particle as a function of time t after its projection. 13. A pipe of diameter D is connected to a water tank of large cross-sectional area in which water is maintained at a height H as shown in the figure. A nozzle of diameter d fitted at the end of the pipe discharges water into the atmosphere. Find the flow rate, given that the density of water is . Also find pressure at point C. (P0 is the atmospheric pressure.) C P0 h H D d 14. A standing wave y = 2A sin kx cos t is set up in the conducting wire of length fixed at both ends by two vertical walls. There is a constant magnetic field B directed into the plane of paper between the walls as shown in the figure. If the wire is vibrating in third harmonic, find the magnitude of maximum emf induced in the wire. B P ***** FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. Q X

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