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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , ALL INDIA TEST SERIES, IIT - JAM – 2019 (Physics), PART TEST – 02, Topic: Mechanics and General Properties of Matter, 20-09-2019, , TIME: 3 HOURS, , MAXIMUM MARKS: 100, , Section A: This section contains a total of 30 Multiple Choice Questions (MCQ), carrying one or two marks each. Each MCQ type question has four choices out of which, only one choice is the correct answer., There will be negative marking @, , 1 rd, 2, for one marks MCQ and rd negative marks, 3, 3, , for two marks MCQ for each wrong answer., Section B: This section contains a total of 10 Multiple Select Questions (MSQ) carrying, , two marks each. Each MSQ type question is similar to MCQ but with a difference that, there may be one or more than one choice(s) that are correct out of the four given, choices. The candidate gets full credit if he/she selects all the correct answers only and no, wrong answers., Section C: This section contains a total of 20 Numerical Answer Type (NAT) questions, , carrying one or two marks each. For these NAT type questions, the answer is a signed, real number which needs to be entered using the virtual keyboard on the monitor. No, choices will be shown for these types of questions., Note: There will be no negative marking for Section B and Section C., , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 1

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, Multiple Choice Questions (MCQ), Q1-Q10 Carry One Mark each. (1/3 negative marks for each wrong answer), , Q1., , A particle of unit mass moves along the x -axis under the influence of a potential,, V  x   x  x  4  . The particle is found to be in stable equilibrium at the point. The, 2, , angular frequency of oscillation of the particle is, (b), , (a) 2, Q2., , 8, , (c), , 1, 2, , (d), , 1, 8, , A block P of mass m is placed on a horizontal frictionless plane. A second block of, same mass m is placed on it and is connected to a spring of constant, k . The two blocks are pulled by distance A . Block Q oscillates, , Q, , s, , P, , without slipping. What is the maximum value of frictional force, between the two blocks?, (a), Q3., , kA, 2, , (c) s mg, , (b) kA, , A particle motion in the, , x y, , (d) zero, , plane is governed by its position vector, , r  a sin  tiˆ  b cos  t ˆj where a, b and  are positive constants and a  b . What is the, , trajectory of the particle?, (a) A parabola, Q4., , (b) A hyperbola, , (c) An ellipse, , (d) A circle, , Which one of the following diagrams correct depicts the variation of kinetic energy  K  ,, potential energy U  and total energy  E  of a body in circular planetary motion?, ( r is the radius of the circle)., K, , (a), , r, , (b), , K, E, , r, , E, U, , U, , U, , K, r, , r, , (c), , (d), , E, , U, , K, , E, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 2

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q5., , If R is the radius of the earth,  is mean density and G is the gravitational constant,, then the earth’s surface potential will be nearly equal to, (a), , Q6., ,  G, R, , 4, (b)   R 3  G, 3, , 2, , 4, (c)   R 2G, 3, , (d), , 4 R,  G, 3 , , , , , , Two bodies of mass 100 kg and 20 kg are moving with velocities 2iˆ  7 ˆj  3kˆ and, ,  10iˆ  35 ˆj  3kˆ  m / s respectively. The velocity of the centre of mass is given by, , Q7., , Q8., , , , , , (a) 2kˆ m / s, , (b) 8iˆ  28 ˆj m / s, , 35 ˆ,  10, , (c)  iˆ , j  3kˆ  m / s, 6,  2, , , (d) 2kˆ cm / s, , , The potential energy function associated with the force F  4 xyiˆ  2 x 2 ˆj is, , (a) U  2 xy 2  constant, , (b) U  2 x 2 y  constant, , (c) U  2 x 2 y  constant, , (d) U  2 xy 2  constant, , From a given sample of uniform wire two circular loops P and Q are made, P of radius, r and Q of radius nr . If the M.I. of Q about its axis is four times that of P about its, , axis, the value of n is, , Q9., , 2, , 1, , 1, , 1, , (a) 4 3, , (b) 4 3, , (c) 4 2, , (d) 4 4, , The centre of a wheel rolling on a plane surface moves with speed v0 . A particle on the, rim of the wheel at the same level as the centre will be moving at speed:, (a) zero, , Q10., , (b) v0, , (c), , 2v0, , (d) 2v0, , A uniform chain of length L and mass M is lying on a table and the coefficient of, friction is  . The maximum length of part of chain hanging over the table such that the, chain does not slide is:, (a), , L, 1 , , (b), , L, 1 , , (c), , L, 2, , (d), , L, 2, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 3

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, Multiple Choice Questions (MCQ), Q11-Q30 Carry Two Mark each. (1/3 negative marks for each wrong answer), , Q11., , x 2 x3, The potential is given by V  x  ,  . Which one of the following is a correct plot of, 2, 3, , V  x ?, , V  x, , (a), , V  x, , (b), x, , V  x, , (c), , x, , V  x, , (d), , x, , x, , Q12. A smooth block is released at rest on a 450 incline and then slides a distance d . If the, time taken to slide on rough incline is n times as large as that to slide on a smooth, incline, the coefficient of friction is, (a), , Q13., , n 1, n, , (b), , n2, n2, , (c), , n4, n3, , (d), , n2  1, n2, , If the gravitational force is assumed to vary inversely as the nth power of distance r ,, then how does the time period of a, planet the sun depend upon r ?, (a) r n, , Q14., , (b) r  n, , (c) r  n 1 / 2, , (d) r  n 1 / 2, , A thin uniform rod of mass M and length L is positioned vertically above an, anchored frictionless pivot point, as shown above, and then allowed to fall to the, ground. With what speed does the free end of the rod strike the ground ?, (a), , 1, gL, 3, , (b), , gL, , (c), , 3 gL, , (d) 12 gL, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 4

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q15., , Match the following List I with List II., List I, , List II, , A. Eccentricity e  0, energy  E   0, B. Eccentricity e  1 E  0, , 1. Circular orbit, 2. Elliptical orbit, , C. e  1, E  0, , 3. Parabolic orbit, , mk 2, D. e  0, E   2, 2J, , 4. Hyperbolic orbit, , A, , B, , C, , D, , (a), , 1, , 2, , 3, , 4, , (b), , 2, , 1, , 3, , 4, , (c), , 3, , 4, , 1, , 2, , (d), , 4, , 3, , 2, , 1, , Q16. From a circular disc of radius R and mass 9 M a small disc of, radius, , R, is removed from the disc. The moment of inertia of the, 3, , 2R/3, , remaining disc about an axis perpendicular to the plane of the disc, and passing through O is, , O, R, , (a) 4MR 2, , (b), , 40, MR 2, 9, , (c) 10 MR 2, , (d), , 37, MR 2, 9, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 5

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q17., , Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbor,, as shown in the figure above. Each penny is a uniform disk of mass m and radius r ., What is the moment of inertia of the system of seven pennies about an axis that passes, through the center of the central penny and is normal to the plane of the pennies?, (b) 29 / 2 mr 2, , (a) 13 / 2 mr 2, Q18., , (c) 49 / 2 mr 2, , (d) 55 / 2 mr 2, , A particle is initially at rest at the top of a curved frictionless track. The x- and ycoordinates of the track are related in dimensionless units by y , , x2, , where the positive, 4, , y-axis is in the vertical downward direction. As the particle sides down the track, what is, its tangential acceleration?, (a), Q19., , 2g, , (b), , x2  4, , gx, 2, , (c), , A particle moves in a potential V  r   V0 e  , , 2 2, , r, , gx, , (d), , x2  4, , gx 2, x 2  16, , . For the given potential it turns out that, , if L is too large, then no circular orbit exists. Then the largest value of L for which a, circular orbit does in fact exist is given by, 1/ 2, , (a) Lmax, ,  2mV ,  2  2 20 ,  e , , (c) Lmax, ,  2mV ,   2 20 ,  e , , 1/ 2, , (b) Lmax, ,  mV ,  2  2 02 ,  e , , (d) Lmax, ,  mV ,   2 02 ,  e , , 1/ 2, , Q20., , 1/ 2, , A stick of length l and mass M initially upright on a frictionless table, starts falling., Then the center of mass will follow the path, (a) Straight line, , Q21., , (b) Parabola, , (c) Hyperbola, , (d) Circular, , A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane, about an axis passing through its centre and perpendicular to its plane with an angular, velocity  . Another disc of the same dimensions but of mass M / 4 is placed gently on, the first disc coaxially. The angular velocity of the system now is, (a)  / 5, , (b) 2 / 5, , (c), , 2, 5, , (d), , 4, 5, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 6

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q22., , A particle of mass m is projected with a velocity v 0 making an angle of 300 with the, horizontal. The magnitude of the angular momentum of the projectile about the point of, projection when the particle is at its maximum height h is:, (a), , Q23., , , , 3mv03, 16 g, , (b) mv03 / 4 2 g, , , , (c) mv03 /, , , , 2g, , , , (d) m 2gh 3, , A projectile of mass 3m is projected with 20 2 m / sec at 450 with ground. At highest, point it explodes in 2 pieces of 2 m and 1m . Mass 2 m falls at a distance of 100 m from, point of projection. The distance of second mass from point of projection where it strikes, the ground is ( g  10 m / sec2 ), (a) 40 m, , Q24., , (b) 20 m, , (c) 30 m, , (d) 10 m, , If the moment of inertia of a disc about an axis tangentially and parallel to its surface be, I, then what will be the moment of inertia about the axis tangential but perpendicular to, the surface:, (a), , Q25., , 6, I, 5, , (b), , 3, I, 4, , (c), , 3, I, 2, , (d), , 5, I, 4, , Four particle of equal mass M move along a circle of radius R under the action of their, mutual gravitational attraction. The speed of each particle is:, , Q26., , (a), ,  Gm , , ,  R , , (b), ,  2 2.GM , , , R, , , , (c), ,  GM, ,  R, , (d), ,  GM, , 2 2 1 , ,  R, , ,  2 2  1 , , ,  4 , , , , , , A cubical block of side a is moving with velocity v on a horizontal smooth plane as, a, shown in the figure., C, v, It hits a ridge at point O ., a, M, The angular speed of the block after it hits O is given by, O, v, 3v, v, 3v, (a)  , (c)  , (b)  , (d)  , a, 2a, 4a, 4a, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 7

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q27., , An interstellar object has speed v at the point of its shortest distance R from a star of, much larger mass M . Given v 2  4GM / R , the trajectory of the object is, (a) circle, , Q28., , (b) ellipse, , (c) parabola, , (d) hyperbola, , The kinetic energy of a satellite in its orbit around the earth is E . What should be the, kinetic energy of the satellite so as to enable it escape from the gravitational pull of the, earth?, (a) 4E, , (b) 2E, , (c), , 2E, , (d) E, , Q29. A constant power P is applied to a particle of mass m . The distance traveled by the, particle when its velocity increases from v1 to v2 is (neglect friction), , Q30., , (a), , 3P 2 2,  v2  v1 , m, , (b), , m,  v2  v1 , 3P, , (c), , m 3 3,  v2  v1 , 3P, , (d), , m 2 2,  v2  v1 , 3P, , Water drops fall at regular intervals from a roof. At an instant when a drop is about to, leave the roof , the separations between 3 successive drops below the roof are in the ratio:, (a) 1: 2 : 3, , (b) 1: 4 : 9, , (c) 1: 3 : 5, , (d) 1: 5 :13, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 8

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, Multiple Select Type Questions (MSQ), Q31-Q40 Carry Two Marks each (No negative marking for any wrong answer), , Q31., , Consider a solid sphere and hollow sphere of same mass M and same radius R . Their, centres are at a distance d from each other., , A, , C, R, , D, , M, , O, , O, , M, , R, , B, Line AB bisects OO  and line CD is tangent to both sphere, then, (a) The moment of inertia of the system about the axis AB is, , 5, MR 2  Md 2, 7, , (b) The moment of inertia of the system about the axis CD is, , 8, MR 2  3MR 2, 16, , 16, Md 2, 2, (c) The moment of inertia of the system about the axis AB is, MR , 15, 2, (d) The moment of inertia of the system about the axis CD is, Q32., , 16, MR 2  2MR 2, 15, , A uniform bar of length 6 a and mass 8 m lies on a smooth horizontal table. Two point, masses m and 2m moving in the same horizontal plane, with speed 2v and v respectively, strike the bar as, , m, 2V, , O,8m, , shown and stick to the bar after collision. Denoting, angular velocity, total energy and centre of mass, velocity by  , E and vc respectively, we have, (a) v  0, , (b)  , , 3v, 5a, , (c)  , , v, 5a, , 2 m, V, , (d) E , , 3mv 2, 5, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 9

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q33., , A net force Fx  t   A  Bt 2 in the  x direction is applied to a boy of mass m . The force, starts at t  0 and continues until time t, (a) Impulse of the force is 2Bt, (c) Impulse of the force is At , , Q34., , (b) His speed at time t is, B 3, t, 3, , (d) Speed at time t is, , A, B 3, t, t, m, 3m, , 2B, t, m, , Equilateral triangle ABC formed from a uniform wire has two small identical beads, initially located at A . The triangle is set rotating about the vertical axis AO . Then the, beads are released from rest simultaneously and allowed to slide down, one along AB and, the other along AC as shown. Neglecting frictional effects, the quantities that are, conserved as the beads slide down are, , Q35., , (a) angular velocity is conserved, , (b) kinetic energy is conserved, , (c) total energy is conserved, , (d) angular momentum is conserved, , A small particle of mass m is at rest on a horizontal circular platform that is free to rotate, about a vertical axis through its center. The particle is located at a radius r from the axis,, as shown in the figure. The platform begins to rotate with constant angular acceleration, ,  .Because of friction between the particle and the platform, the particle remains at rest, with respect to the platform. When the platform has reached angular speed  , the angle, between the static frictional force f s and inward radial direction is  . Then which of the, , , , following options are correct?, (a)  , , fs, mr, , (b)  , , , (c)   tan 1 , , , 2, , , , , , f s sin , mr, ,  , (d)   tan 1  2 ,  , , , r, , fs, , m, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 10

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q36., , , , , , , A particle of mass m, moving with a velocity v  v0 iˆ  ˆj , collides elastically with, , another particle of mass 2m which is at rest initially. Here, v 0 is a constant. Which of the, following statements is Incorrect?, , , , , (a) The velocity with which the centre of mass moves before collision is v  v 0 iˆ  ˆj, , , , (b) The speed of the particle of mass m before collision in the center of mass frame, is 2v0 ., (c) After collision the speed of the particle with mass 2m in the centre of mass frame is, 2, v0 ., 3, (d) The speed of the particle of mass 2m before collision in the center of mass frame, is 2v0 ., Q37., , Consider a particle of mass m following a trajectory given by x  x0 cos 1t and, , y  y0 sin 2t , where x0 , y0 , 1 and 2 are constants of appropriate dimensions. Then, which of the following is correct?, (a) The force is always central force, (b) Angular momentum about z axis is conserved if x0  y0 and 1  2, (c) Angular momentum about z axis is conserved if x0  y0 and 1  2, (d) Angular momentum about z axis is conserved if and x0  y0 and 1  2, Q38., , An artificial satellite moving in circular orbit around the earth has a total (kinetic +, potential) energy E0 . Then which of the following is correct, (a) The kinetic energy is  E0, , (b) The potential energy is 2E0, , (c) Total energy E0 is negative, , (d) Total angular momentum is conserved., , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 11

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q39., , A thin uniform rod of mass m and length l is free to rotate about is upper end. When it is, at rest, it receives an impulse I at its lowest point, normal to its length. Immediately after, impact,, (a) The angular momentum of the rod about its upper end is I , (b) The angular velocity of the rod is 3I / m, (c) The kinetic energy of the rod is 3I 2 / 2m, (d) The linear velocity of the midpoint of the rod is 3I / 2m, , Q40., , A liquid flows through a horizontal tube. The velocities of the liquid in the sections,, which have areas of cross-section A1 and A2 are v1 and v2 respectively. The difference, in the levels of the liquid in the two vertical tubes is h . Which of the following, statements is/are true?, h, , A1, , v1, , v2, , A2, , (a) The volume of the liquid flowing through the tube in unit time is A1v1, (b) v2  v1  2 gh, (c) v22  v12  2 gh, (d) The total energy per unit mass of the liquid is the same in both sections of the tube., , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 12

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, Numerical Answer Type Questions (NAT), Q41-Q50 Carry One Mark each (No negative marking for any wrong answer)., , Q41., , A block slides down an incline at angle 300 with an acceleration, , g, . The kinetic friction, 4, , coefficient is ___________________., Q42., , A comet moves in an elliptical orbit with an eccentricity of e  0.20 around a star. The, distance between the perihelion and the aphelion is 1.0  10 km . If the speed of the comet, at perihelion 60 km / s then the speed of the comet at the aphelion is____________ km / s, , Q43., , A body of mass m moves under the action of a central force with potential, V  r   Ar 3  A  0  where r is the distance from the origin. If the particle moves in a, , circle of radius R and its kinetic energy is  AR 3 , then the value of  is_____________, Q44., , A body of mass 10 kg is being acted on by a force of 3t 2 N and an opposing constant, force of 32 N . The initial speed is 10 m / s . The velocity of the body after 5 seconds is, ,  m / sec then the value of  is________________, Q45., , A disc rolls over a horizontal floor without slipping with a linear speed of 5 cm / sec ., Then the linear speed of a particle on its rim, with respect to the floor, when it is in its, highest position is  .cm / sec then value of  is____________________, , Q46., , Block A has a mass of 5 kg and is placed on top of a smooth, , A, , triangular block B having a mass 30kg . Neglect the size of, , B, , block A . If the system is released from rest, the distance that, B moves when A reaches the bottom is______________ mm, , 300, 0.5m, , Q47., ,  x2 , A cylindrical rod of length L has a mass density distribution given by   x   0 1  2  ,,  L , , where x is measured from one end of the rod and  0 is a constant of appropriate, dimensions. If the centre of mass of the rod is at a distance  L from that end then, value of  is____________________, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 13

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q48., , A bullet of mass m  1 kg hits a target of mass M  10 kg hanging by a string and gets, embedded in it. If the block rises to a height of h  4.9 m as a result of this collision, the, velocity of the bullet before collision is________________ m / s, , Q49., , Water flows in a horizontal tube as shown below. The pressure of water changes by, 900  / m2 between A and B where the area of cross section are 40 cm 2 and 20 cm 2, respectively. The velocity of fluid at A is__________________________ cm / sec ., A, B, , Q50., , A particle of mass 1 kg is moving along the line y  x  2 (here, x and y are in meters), with speed 2 m / s . The magnitude of angular momentum of particle about origin, is___________________ kgm 2 / sec, , (answer must be in integer value), , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 14

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, Numerical Answer Type Questions (NAT), Q51-Q60 Carry Two Mark each (No negative marking for any wrong answer)., , Q51., , A cubical block of wood of edges 3cm float in water. The lower, , w, w, , surface of the cube just touches the free end of a vertical spring, fixed at the bottom of the pot. The maximum weight that can be put, on the block without wetting it is ________________ N, , T, , (density of wood = 800 kg / m and spring constant  50 N / m ), 3, , Q52., , Fr, , A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane, about an axis passing through its centre and perpendicular to its plane with an angular, velocity 10 rad / s . Another disc of same dimensions but of mass, , M, is placed gently on, 4, , the first disc coaxially. The angular velocity of the system now is __________ rad / s ., Q53., , The coefficient of static friction between a small coin and the surface of a turntable is, 0.30. The turntable rotates at 33.3 revolutions per minute. What is the maximum distance, from the center of the turntable at which the coin will not slide is_______________, , Q54., , For the system consisting of the two blocks shown in the figure below, the minimum, horizontal force F is applied so that block B does not fall under, the influence of gravity. The masses of A and B, are, , 16.0, , kilograms, , and, , 4.0, , kilograms,, , F, , A, , B, , respectively. The horizontal surface is frictionless, and the coefficient, of friction between the two blocks is, , 0.50 . Then the magnitude of, , F, , is_____________________ N (Take 10m / sec 2 ), Q55., , A billiard ball, initially at rest, is given a sharp impulse by a rod. The rod is held, horizontally at a height h above the centre of the ball. The ball immediately begins to roll, without slipping after the impact. The height h   r, , then the value of , , is____________, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 15

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fiziks, Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics, , Q56., , A body is moved along straight line by a machine delivering constant power. The, distance moved by the body in time t is proportional to t then, , value of , , is________________, Q57., , The ratio of earth’s orbital angular momentum (about the sun) to its mass is, 4.4 1015 m 2 / s . The area enclosed by earth’s orbit is approximately__________ 1022 m 2 ., , Q58., , A ball of mass m moves at speed v and makes head on collision with identical ball at, rest. Kinetic energy of the balls after collision is, , 3, of original kinetic energy. The value, 4, , of e is_________________(Upto two digits after decimal), Q59., , A uniform chain of mass m and length l hangs on a thread and, touches the surface of a table by its lower end. If the force exerted, by the table on the chain when half of its length has fallen is  mg ,, then the value of  is_______________(The fallen part does not, form heap)., , Q60., , Water level is maintained in a cylindrical vessel upto a fixed height H . The vessel is kept, on a horizontal plane. At  H height above the bottom should a hole be made in the, vessel so that the water stream coming out of the hole strikes the horizontal plane at the, greatest distance from the vessel then value of  is_____________, ------------------------------------------------------------------------------------------------------------, , H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016, Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com | Email: [email protected], , Revised Edition 2019, , 16