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Rotational Motion, , Moment of Inertia, , Moment of inertia basic (Level 0), , [Rotational motion], , Page 2

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1. Generally the mass of a fly wheel is concentrated, in its rim in order to, (a) decrease the moment of inertia, (b) increase the moment of inertia, (c) obtain stable equilibrium, (d) obtain a strong wheel, 2. Mass in linear motion has its analogue in rotational, motion, (a) moment of inertia, (b) torque, (c) weight, (d) angular momentum, 3. The moment of inertia of a uniform semicircular, wire of mass M and radius r about a line, perpendicular to the plane of the wire through, the centre is, (a) Mr2, , (b), , 1, 1, Mr 2 (c) Mr 2 (d) (2/5)Mr2, 2, 4, , 4. Let I1 and I2 be the moments of inertia of two, bodies of identical geometrical shape, the first, made of aluminium and the second of iron., (a) I1 < I2, (b) I1 > I2, (c) I1 > I2, (d) relation between I1 and I2 depends on the, actual shapes of the bodies., 5. The moment of inertia of a thin uniform rod of, mass M and length l about an axis perpendicular, to the rod, through its centre is I. The moment of, inertia of the rod about an axis perpendicular to, the rod through its end point is, (a) I/4 (b) I/2, (c) 2I, (d) 4I, 6. If solid sphere and solid cylinder of same radius, and density rotate about their own axes, the, moment of inertia will be greater for (L=R), , [Rotational motion], , (a) solid sphere, (b)solidcylinder, (c) both, (d) equal both, 7. If M mass is the mass of a disc and r is its radius, of gyration, then moment of inertia is given by, (a) Mr2, (b) (1/2) Mr2, 2, (c) (2/5) Mr, (d) (2/3) Mr2, 8. The moment of inertia of a disc about its, diameter is I. Moment of inertia about an axis, passing through its circumference and parallel to, diameter will be, (a) 4I, (b) 6i, (c) 3I, (d) 5I, 9. The moment of inertia of a regular disc with, respect to the axis passing through one of its, edges and perpendicular to its plane (M and R be, the mass and radius of disc) is, 1, 2, 3, (a) MR² (b) MR² (c) MR² (d) MR2, 2, 3, 2, 10. What is the moment of inertia of a ring about, tangent axis in its plane, (a) MR², (b) 2MR², (c) 3/2 MR², (d) none of these, 11. If the moment of inertia of a ring about a, tangential axis perpendicular to its plane is I1 and, about its diameter is I2 then the value of I1:I2 will, be, (a) 4:1 (b) 1:4, (c) 3:4, (d) 3:2, 12. A thin wire of, x, length L and, 900, uniform linear, mass density ρ is, O, bent into a circular, loop with centre at, O as shown. The moment of inertia of the loop, about the axis XX’ is, (a) (ρL3)/(8π2 ), (b) (ρL3)/(16π2 ), 3, 2, (c) (5ρL )/(16π ), (d) (3ρL3)/(8π2 ), 13. One quarter sector is cut from a uniform circular, disc of radius R. This, sector has mass M. It is, made to rotate about a, line perpendicular to its, plane and passing, through the centre of, the original disc. Its, moment of inertia about, the axis of rotation is :, (a) 1/2 MR2, (b) 1/4 MR2, 2, (c) 1/8 MR, (d) √2MR2, 14. Consider a uniform square plate of side ‘a’ and, mass ‘m’. The moment of inertia of this plate, about an axis perpendicular to its plane and, passing through one of its corners is, (a), , 5, 2, 1, 7, ma 2 (b), ma 2 (c), ma 2 (d) ma 2, 6, 3, 12, 12, , 15. For the given uniform, square lamina ABCD,, whose centre is O,, (a) IAC =, (b), , D, , 2 IEF, , F, , C, , O, , 2 IAC = IEF, A, , E, , Page, B 3

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(c) IAD = 3IEF, (d) IAC = IEF, 16. The moment of inertia of a uniform semicircular, disc of mass M and radius r about a line, perpendicular to the plane of the disc through the, centre is, (d) Mr2, , thickness t/4. The relation between of moments, of inertia IA and IB is, (a) IA >IBm, (b) IA =IB (c) IA <IB, (d) depends on the actual value of t and r, 25. Four point masses, each of value m, are placed at, the corners of a square ABCD of side l. The, moment of inertia of this system about an axis, passing through A and parallel to BD is, , 17. One solid sphere A and another hollow sphere B, are of same mass and same outer radii. Their, moment of inertia about their diameters are, respectively IA and IB such that, (a) IA < IB, (b) IA > IB, (c) IA = IB, (d) IA/IB = dA/dB, Where dA and dB are their densities., 18. Moment of inertia of a circular wire of mass M, and radius R about its diameter is, (a) MR2/2 (b) MR2, (c) 2MR2 (d) MR2/4., 19. The moment of inertia of a sphere of mass M and, radius R about an axis passing through its centre, is 2/5 MR2. The radius of gyration of the sphere, about a parallel axis to the above and tangent to, the sphere is, 7, 3, 3, 7, (a) R, (b) R, (c), (d), R, R, 5, 5, 5, 5, 20. Four identical thin rods each of mass M and, length 1, form a square frame. Moment of inertia, of this frame about an axis through the center of, the square and perpendicular to its plane is:, , (a) 2ml2 (b) 3 ml2, (c) 3ml2, (d) ml2, 26. A circular disc X of radius R is made from an, iron pole of thickness t, and another disc Y of, radius 4R is made from an iron plate of thickness, t/4. then the relation between the moment of, inertia IX and IY is, (a) IY  32IX, (b) IY  16IX, (c) IY = IX, (d) IY  64 IX, 27. A wire of mass m and length l is bent in the form, of a quarter circle. The moment of inertia of this, wire about an axis passing through the centre of, the quarter circle and perpendicular to the plane, of the quarter circle is approximately, (a) 0.6 ml2, (b) ml2, 2, (c) 0.2 ml, (d) 0.4 ml2, 28. One quarter section is cut from a uniform, circular disc of radius R. This section has a mass, M. It is made to rotate a line perpendicular to its, plane and passing through the center of the, original disc. Its moment of inertia about the axis, of rotation is, , (a), , 2, Mr 2 ., 5, , (b), , 1, M 12, 3, 2, (c) M 12, 3, (a), , 1, Mr, 4, , (c), , 1, Mr 2, 2, , 4, M 12, 3, 13, M 12, (d), 3, (b), , 21. Four particles each of mass m are placed at the, corners of a square of slide length l. The radius, of gyration of the system about an axis, perpendicular to the square and passing through, centre is, l, l, (a), (b), (c) l, (d) 2l, 2, 2, 22. Length width and mass of a rectangular plate are, l, b and m respectively. The radius of gyration, about the axis passing through centre and, perpendicular to the plane is, (a), , l 2  b2, 2, , (b), , l 2  b2, 3, , (d), , l 2  b2, 8, , l 2  b2, 12, 23. Mass and the moment of inertia with respect to, diameter of solid and a hollow sphere are same., The ratio of their radii will be, (a) 1:2, (b) 3:2 (c) 5:3, (d) 5:4, 24. A circular disc A of radius r is made from an, iron plate of thickness t and another circular disc, B of radius 4r is made from an iron plate of, , (c), , [Rotational motion], , (a), , 1, 1, 1, MR 2 (b) MR 2 (c) MR 2 (d), 8, 2, 4, , 2MR2, , 29. A thin rod of length L and mass M, is bend, O, at, the middle point O as shown, figure. Consider an axis, , passing through two middle, point O and perpendicular, to the plane of the bend rod. Then moment of, inertia about this axis is:, (a) 2 / 3mL2, (b) 1/ 3mL2, 2, 2, (c) 1 / 12mL, (d) 1/ 24mL, 30. A solid cylinder of mass 1 kg and radius 10 cm is, rotating about its natural axis. What is the, moment of inertia of cylinder?, (a) 5kg  m2, (b) 5 103 kg  m2, (c) 10kg  m2, (d) None of these, 31. A ring of mass M and radius R is suspended, from a horizontal nail in a vertical wall in a, room. The moment of inertia of the ring about, the nail is, (a) MR 2, (b) 2MR 2, 2, (c) 4MR 2, (d) 8MR, 32. The moment of inertia of a thin uniform circular, disc about one of the diameters is l. Its moment, of inertia about an axis perpendicular to the plane, of the disc and passing through its centre is, , Page 4

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2l, , (a), (c), , I, 2, , (b) 2I, (d), , I, 2, , 33. The ratio of the radii of gyration of a circular disc, to that of a circular ring, each of same mass and, radius around their respective axes is:, (a) 2 :1, (b) 2 : 3, , (c) 3 : 2, (d) 1: 2, 34. What is the moment of inertia for a solid sphere, w.r.t a tangent touching to its surface?, 7, 2, MR 2, (a), (b) MR 2, 5, 5, 2, 5, MR 2, (c), (d) MR 2, 3, 3, 35. The moment of inertia of a thin uniform rod of mass, M and length L about an axis passing through its, midpoint and perpendicular to its length is I0. Its, moment of inertia about an axis passing through one, of its ends and perpendicular to its length is:, , ML2, 2, (c) I0 + 2ML2, (a) I0 +, , 16 2, mr, 5, 11 2, (d), mr, 5, , (a) 3 mr2, , (b), , (c) 4 mr2, , 38. A light rod of length l has two masses m1 and m2, attached to its two ends. The moment of inertia of the, system about an axis perpendicular to the rod and, passing through the centre of mass is:, (a) (m1 + m2) l2, , m1m2 2, l, m1  m2, , (c), , ML2, 4, (d) I0 + ML2, , (a) D, , (b) A, , (c) B, , (d) C, , 37. Three identical spherical shells, each of mass m and, radius r are placed as shown in figure. Consider an, axis XX’ which is touching to two shells and passing, through diameter of third shell. Moment of inertia of, the system consisting of these three spherical shells, about XX’ axis is:, , (d), , m1  m2 2, l, m1m2, , o, (a) 3 MR2, , (b), , 2, MR 2, 3, , (c) MR2, , (d), , 4, MR 2, 5, , 40. The moment of inertia of a solid sphere, about an, axis parallel to its diameter and at a distance of x, from it, is I(x)’. which one of the graphs represents, the variation of I(x) with x correctly?, I(x), , I(x), (a), , (b), , O, , x, , O, , x, I(x, , I(x), , (d), , (c), , O, , [Rotational motion], , m1m2 l 2, , 39. A circular disc D1 of mass M and radius R has two, identical discs D2 and D3 of the same mass M and, radius R attached rigidly at its opposite ends (see, figure). The moment of inertia of the system about, the axis OO’, passing through the center of D1 as, shown in the figure, will be:, , (b) I0 +, , 36. The moment of inertia of a uniform circular disc is, maximum about an axis perpendicular to the disc and, passing through:, , (b), , x, , O, , x, , Page 5

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Kinematics of rotational Motion, Single choice questions (Level 0), 41. A pulley one metre in diameter rotating at 600, revolutions a minute is brought to rest in 80 sec by a, constant orce of friction on its shaft. How many, revolutions does it make before coming to rest?, (a) 200, (b) 300, , (c) 400, , (d) 500, , 42. Which of the following statements is false for a, particle moving in a circle with a constant angular, speed?, (a) The velocity vector is tangent to the circle., (b) The acceleration vector is tangent to the, circle, (c) The acceleration vector points to the centre, of the circle., (d) The velocity and acceleration vectors are, perpendicular to each other., 43. The direction of the angular velocity vector is along:, (a) The tangent to the circular path, (b) The inward radius, (c) The outward radius, (d) The axis of rotation, 44. A wheel has angular acceleration of 3.0 rad/sec2 and, initial angular speed of 2.00 rad/sec. In a time of 2, sec it has rotation through an angle (in radian) of, (a) 4, (b) 6, , (c) 10, , (d) 3.0, , 46. A wheel having moment of inertia 2 kg-m2 about its, vertical axis, rotates at the rate of 60 rpm about an, axis. The torque which can stop the wheel’s rotation, in one minute would be:, , [Rotational motion], , (c), , , 12, , , , 18, , N m, N m, , , , N m, 15, 2, (d), N m, 15, (b), , 47. The instantaneous angular position of a point on a, rotating wheel is given by the equation,  (t)  2 t 3  6t 2 . The toque on the wheel becomes, zero at:, (a) T = 1 s, (b) t = 0.5 s, , (c) T = 0.25 s, , (d) t = 2 s, , 48. A solid cylinder of mass 2 kg and radius 4 cm is, rotating about its axis at the rate of 3 rpm. The toque, required to stop after 2  revolutions is:, (a) 2 106 Nm, (b) 2 103 Nm, 4, (c) 12 10 Nm, (d) 2 106 Nm, , Torque concepts, Single choice questions (Level 0), 49. Figure shows a small wheel fixed co axially on a, bigger one of double the radius. The system rotates, about the common axis. The string supporting A and, B do slop on the wheels. If x and y be the distance, travelled by A and B in the same time interval, then, , (d) 12, , 45. A uniform circular disc of radius 50 cm at rest is free, to turn about an axis which is perpendicular to its, plane and passes through its centre. It is subjected to, a torque which produces a constant angular, acceleration of 2.0 rad s-2. Net acceleration of a, particle situated at periphery in ms-2 at the end of 2.0, s is approximately:, (a) 8.0, (b) 7.0, , (c) 6.0, , (a), , (a) X = 2y, , (c) y = 2x, , (b) x = y, , (d) none of these, , 50. A door 1.6 m wide requires a force of 1 N to be, applied at the free end to open or close it. The force, that is required at a point 0.4 m distant from the, hinges for opening or closing the door is:, (a) 1.2 N, (b) 3.6 N, , (c) 2.4 N, , (d) 4 N, , Page 6

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51. Let F be the force acting on particle having position, vector r and  be the torque of this force about the, origin.Then:, (a) r.  0 and F .  0, (b) r.  0 and F .  0, (c) r.  0 and F .  0, (d) r.  0 and F .  0, 52. A uniform rod of length l and mass m is free to rotate, in a vertical plane about A. the rod initially in, horizontal position is released. The initial angular, acceleration of the rod is (Moment of inertia of rod, about A is, , ml 2, ):, 3, , g, 2l, g, (c), 13l, (a), , 7g, 3l, , (b), , (d), , g, 3l, , 57. The magnitude of torque on a particle of mass 1 kg is, 2.5 Nm about the origin. If the force acting on it is, 1N, and the distance of the particle from the origin is, 5 m, the angle between the force and the position, vector is (in radius):-, , , 8, , (c), 4, , , 6, , (d), 3, , (a), , (b), , Work energy application, 3g, 2l, 3g, (c) 2, 2l, (a), , (b), , 2l, 3g, , (d) mg, ^, , ^, , l, 2, , ^, , 53. A force (5 i  7 j  3 k ) N acts on a particle at, ^, , ^, , ^, , position (i  j  k ) m . Find torque of this force on, the particle about origin., ^, , ^, , ^, , (a) (4 i  2 j  2k ) N m, ^, , ^, , ^, , (b) (4 i  2 j  2k ) N m, ^, , ^, , ^, , (c) (4 i  2 j  2k ) N m, ^, , ^, , (d) 157 N, , 55. A rope is wound around a hollow cylinder of mass, 3kg and radius 40 cm. what is the angular, acceleration of the cylinder if the rope is pulled with, a force of 30 N?, (a) 0.25 rad/s2, (b) 25 rad/s2, , (c) 5 m/s2, , (c) mr2  2, , 1, mr 2, 2, 1, (d) mr 2 2, 2, (b), , 59. A rod of length L is hinged from one end. It is, brought to a horizontal position and released. The, angular velocity of the rod when it is in vertical, position is:, (a), , (c), , 2g, L, g, 2L, , 3g, L, g, (d), L, (b), , 60. A body is rotating with angular velocity 30 rad/s. if, its kinetic energy is 360 J, then its moment of inertia, is:, (a) 0.8 kg m2, (b) 0.4 kg m2, , (c) 1 kg m2, , (d) 1.2 kg m2, , 61. When a stick is released (as shown in figure), its free, end velocity when its strikes the ground is:, , 0.6 m, , (d) 25 m/s2, , 56. A rigid massless rod of ;length 3/has two masses, attached at each end as shown in the figure. The rod, is pivoted at point P on the horizontal axis (see, figure). When released from initial horizontal, position, its instantaneous angular acceleration will, be:, , [Rotational motion], , (a) mr , , ^, , (d) (10 i  8 j  12k ) N  m, 54. A solid cylinder of mass 50 kg and radius 0.5 m is, free to rotate about the horizontal axis. A massless, string is would round the cylinder with one end, attached to it and other hanging freely. Tension in the, string required to produce an angular acceleration of, 2 revolutions s-2 is:, (a) 25 N, (b) 50 N, , (c) 78.5 N, , Single choice questions (Level 0), 58. A ring radius r and mass m rotates about an axis, passing through its centre and perpendicular to its, plane with angular velocity  . Its kinetic energy is:, , (a) 4.2 m/s, , (c) 2.8 m/s, , (b) 1.4 m/s, , (d), , 6m / s, , 62. A solid sphere of mass m and radius R is rotating, about its diameter. A solid cylinder of the same mass, and same radius is also rotating about its geometrical, axis with an angular speed twice that of the sphere., , Page 7

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The ratio of their kinetic energies of rotation (E sphere/, E cylinder) will be., , (a) 1 : 4, (c) 2 : 3, , (b) 3 : 1, (d) 1 : 5, , Angular momentum, Single choice questions (Level 0), 63. Angular momentum is:, (a) A polar vector, (b) An axial vector, (c) A scalar, (d) None of these, 64. A wheel of moment of inertia I and radius R is, rotating about its axis at an angular speed 0 . It, picks up a stationary particle of mass m at its edge., Find the new angular speed of the wheel., (a) 0, , mR 20, (c), I  mR 2, , I 0, I  mR 2, I 0, (d), I  mR 2, , 3, A0, 4, , (c) 3A0, , (b) 4A0, , (d), , 3, A0, 2, , 66. A disc is rotating about its own axis with angular, frequency 100 rpm. When a mass of 100 g is placed, at 10 cm from its centre then its angular frequency, becomes 50 rpm. The moment of inertia of the disc, is:, (a) 5 1014 gcm2, (b) 104 gcm2, , (c) 102 gcm2, , (d) 105 gcm2, , 67. An object of mass ‘m’ is projected with a velocity ’u’, at an angle 450 with the horizontal. When the object, is at maximum height, its angular momentum about, the points of projection is:, , mu 2, (a), g, (c), , mu 3, 4 2g, , mu 2, (b), 2g, (d), , mu u, 2g, , 68. Angular momentum of a particle rotating under a, central force is constant due to:, (a) Constant torque, (b) Constant force, (c) Constant linear momentum., (d) Zero torque, 69. A particle of mass m moves I the X_Y plane with a, velocity  along the straight line AB. If the angular, momentum of the particle with respect to origin O is, LA hen it is at A, and LB when it is at B, then:, , [Rotational motion], , (d) LA < LB, 70. A particle of mass m in moves along line PC with, velocity v as shown. What is the angular momentum, of the particle about O?, , (b), , 65. The angular momentum of a rotating body changes, from A0 to 4A0 in 4 sec. the torque acting on the, body is:, (a), , (a) LA > LB, (b) LA = LB, (b) relationship between LA and LB depends, upon the slope of the line AB, , (a) mvL, , (b) mvl, , (c) mvr, , (d) zero, , 71. A horizontal platform is rotating with uniform, angular velocity around the vertical axis passing, through its centre. At some instant of time a viscous, fluid of mass “m” is dropped at the cnttre and is, allowed to spread out and finally fall. The angular, velocity during this period, (a) Decreases continuously, (a) Decreases initially and increases again, (b) Remains unaltered, (c) Increases continuously, 72. A disc is rotating with angular speed  . If a child sits, on it, what is conserved?, , (a) Linear momentum, (b) Angular momentum, (c) Kinetic energy, (d) Potential energy, 73. A thin circular ring of mass M and radius ‘r’ is, rotating about an axis with a constant angular, velocity  . Four object each of mass m, are gently, placed to the opposite ends of two perpendicular, diameters of the ring. The angular velocity of the ring, will be:, , M, 4m, ( M  4m), (c), M, (a), , M, M  4m, ( M  4m), (d), M  4m, (b), , 74. A round disc of moment of inertia I2 about its axis, perpendicular to its plane and passing through its, centre is placed over another disc of moment of, inertia I1 rotating with an angular velocity  about, the same axis. The final angular velocity of the, combination of discs is, (a), , , , (b), , I1, I1  I 2, , Page 8

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(c), , (I1  I 2 ), I1, , (d), , I2 , I1  I 2, , ^, ^, , 75. Two bodies have their moments of inertia l and 2 l, respectively about their axis of rotation. If their, kinetic energies of rotation are equal, their angular, momentum will be in the ratio:, (a) 1 : 2, , (c) 1: 2, , 2 :1, (d) 2 : 1, (b), , 76. A thin circular ring of mass M and radius r is rotating, about an axis with constant angular velocity  . Two, objects each of mass m are attached gently to the, opposite ends of a diameter of the ring. The ring now, rotates with angular velocity given by:, , 2M , M  2m, M, (c), M  2m, (a), , ^, , 80. A force F   i  3 j  6 k is acting at a point, , 2M , M  2m, ( M  2m), (d), 2m, (b), , 77. A circular disk of moment of inertia It is rotating in a, horizontal plane, but its symmetry axis, with a, constant angular speed i . Another disk of moment, of inertia Ib is dropped co axially onto the rotating, disk. Initially the second disk has zero angular speed., Eventually both the disks rotate with a constant, angular speed  f . The energy lost by the initially, , ^, , ^, , ^, , r  2 i  6 j  12 k . The value of  for which, angular momentum about origin is conserved is:, (a) 1, (b) – 1, , (c) 2, , (d) zero, , 81. Two rotating bodies A and B of masses m and 2m, with moments of inertia IA and IB (IB > IA)have equal, kinetic energy of rotation. If LA and LB be their, angular momenta respectively, then:, , (a) LB > LA, L, (c) LA = B, 2, , (b) LA > LB, (d) LA = 2LB, , 82. A particle of mass 20 g is released with an initial, velocity 5 m/s along the curve from the point A, as, shown in the figure. The point A is at height h from, point B. the particle slides along the frictionless, surface. when the particle reaches point B, its angular, momentum about O will be:-, , [Take g = 10 m/s2], , rotating disc to friction is:, , (a), , 1 Ib It, i2, 2 (It  Ib ), , 1 I t2, i2, (c), 2 (It  Ib ), , (b), , 1 I b2, i2, 2 (It  Ib ), , I I, (d) b t i2, (It  Ib ), , 78. A dancer during rotation folds her hand, due to which, her moment of inertia decreases by 50% then her, final angular velocity will becomes:, , (a) Double, (c) half, , (b) four times, (d) remains same, , 79. A mass m moves in a circle on a smooth horizontal, plane with velocity 0 at a radius R0. The mass is, attached to a string which passes through a smooth, hole in the plane as shown., , (a) 8 kg-m2/s, 2, , (c) 3 kg-m /s, , (b) 6 kg-m2/s, , (d) 2 kg-m2/s, , 83. A thin smooth rod of length L and mass M is rotating, freely with angular speed 0 about an axis, perpendicular to the rod and passing through its, centre. Two beads of mass m and negligible size are, at the center of the rod initially. The beads are free to, slide along the rod. The angular speed of the system,, when the beads reach the opposite ends of the rod,, will be:-, , M 0, M  3m, M 0, (c), M  2m, (a), , M 0, M m, M 0, (d), M  6m, (b), , Equilibrium of rigid bodies, , The tension in the string is increased gradually, and finally moves in a circle of radius, final value of the kinetic energy is:, , 1, m 02, 4, 1, (c) m 02, 2, (a), , (b) 2m 02, , (d) m 02, , R0, . The, 2, , Single choice questions (Level 0), 84. If a ladder is not in balance against a smooth vertical, wall, then it can be made in balance by:, (a) Decreasing the length of ladder, (b) Increasing the length of ladder, (c) Increasing the angle of inclination, (d) Decreasing the angle of inclination, 85. A rod of weight W is supported by two parallel knife, edges A and B and is in equilibrium in a horizontal, position. The knives are at a distance d from each, other. The center of mass of the rod is at a distance d, from A. the normal reaction on A is:, (a), , [Rotational motion], , Wd, x, , (b), , W (d  x), x, , Page 9

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(c), , W (d  x), Wx, (d), d, d, , 86. O is the center of an equilateral triangle ABC., , F1 , F2 and F3 are three forces acting along the sides, AB, BC and AC as shown in figure. What should be, , (a)  > 1, , the magnitude of F3 so that total torque about O is, zero?, , (c)  , , 1, 2, , (b)  <, , 1, 2, , (d)   1, , 90., , (a) F3  F1  F2, , (b) F3  F1  F2, , (c) F3  F1  2 F2, , (d) Not possible, , Two cubes A and B of same shape, size and, mass are placed on a rough surface in the same, manner. Equal forces are applied on both the cubes., But at the cube A, the force is applied at the top in, horizontal direction. But at the cube B just above the, center of mass of the cube in the same manner. Then, (a) A will topple first, (b) B will topple first, (c) Both will topple at the same time, (d) None of the above, 91., What will be the value of maximum, acceleration of the truck in the forward direction so, that the block kept on the back does not topple?, , Toppling, 87. A cone of radius r and height h rests on a rough, horizontal surface, the coefficient of friction between, the cone and the surface being  . A gradually, increasing horizontal force F is applied to the vertex, of the cone. The largest value of  for which the, cone will slide before it topples is, , (a) ag/h, (c) ag/2h, , (b) hg/ a, (d) h / bg, , Rolling, , (a)  , , r, 2h, , (c)  , , r, h, , 2r, 5h, r, (d)  , h, (b)  , , 88. A cubical block of side L rests on a rough horizontal, surface with coefficient of friction  . A horizontal, force F is applied on the block as shown. If the, coefficient of frictions sufficiently high so that the, block does not slide before toppling, the minimum, force required to topple the block is:, , (a) Infinitesimal, , (c) mg/2, , (b) mg/4, , (d) mg(1 -  ), , 89. A force F is applied on the top of a cube as shown in, figure. The coefficient of friction between the cube, and the ground is  . If F is gradually increased, the, cube will toppel before sliding if, , Single choice questions (Level 0), 92. A solid sphere, a hollow sphere and a disc, all having, same mass and radius, are placed at the top of a, smooth incline and released. Least will be taken in, reaching the bottom by, (a) The solid sphere, (b) The hollow sphere, (c) The disc, (d) All will take same time, 93. A sphere cannot roll on, (a) A smooth horizontal surface, (b) A smooth inclined surface, (c) A rough horizontal surface, (d) A rough inclined surface, 94. Figure shows a smooth inclined plane fixed in a car, accelerating on a horizontal road. The angle of, incline  is related to the acceleration a of the car as, a = g tan  . If the sphere is set in pure rolling on the, incline,, , (a) It will continue pure rolling, (a) It will slip down the plane, (b) Its linear velocity will increase, , [Rotational motion], , Page 10

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(c) Its linear velocity will slowly decrease, 95. If a spherical ball rolls on a table without slipping,, the fraction of its total energy associated with, rotation is:, (a) 3/5, (b) 2/7, , (c) 2/5, , 102., A small object uniform density rolls up a curved, surface with an initial velocity  . It reaches up to a, maximum height of, , 3 2, with respect to the initial, 4g, , position, the object is:, , (d) 3/7, , 96. The speed of a homogeneous solid sphere after, rolling down an inclined plane of vertical height h,, from rest without sliding is:, (a), , gh, , (c), , 4,   gh, 3, , (b), , g,   gh, 5, ,  10 ,   gh, 7, , (d), , 97. If a solid sphere, disc and cylinder are allowed to roll, down an inclined plane from the same height:, (a) The cylinder will reach the bottom first, (b) The disc will reach the bottom first, (c) The sphere will reach the bottom first, (d) All will reach the bottom at the same time, 98. A ring is rolling on a rough horizontal surface, without slipping with a linear speed ‘V’ referring to, Fig. ratio of speeds of points B and A is:, , (a) Ring, , (b) solid sphere, , (c) hollow sphere, , (d) disc, , 103., A body rolls down an inclined plane. If its, kinetic energy of rotation is 40% of its kinetic energy, of translation, then the body is, (a) Solid cylinder, (b) Solid sphere, , (c) disc, , (d) ring, , 104., A round uniform body of radius R, mass M and, moment of inertia ‘I’, rolls down (without slipping), an inclined plane making an angle  with the, horizontal. Then its acceleration is:, , g sin , MR 2, 1, I, g sin , (c), MR 2, 1, I, , g sin , I, 1, MR 2, g sin , (d), I, 1, MR 2, , (a), , (a) 1 : 1, , (c), , (b) 1 : 2, , 2 :1, , (d) 1 : 2, , 99. A ring is rolling on a rough horizontal surface, without slipping with a linear speed  . Referring to, figure linear speed of point X is, , (b), , 105., A spherical ball of mass 20 kg is stationary at the, top of a hill of height 100 m. It rolls down a smooth, surface to the ground, then climbs up another hill of, height 30 m and finally rolls down to a horizontal, base at a height of 20 m above the ground. The, velocity attained by the ball is:, , 5, m/ s, 7, (c) 40 m/s, , (b) 20m / s, , (a) 40, (a), ,  sin , , (c) 2 cos, , , 2, , (b) , , (d) 2 sin, , , 2, , 100., A solid cylinder, a circular disc, a solid sphere, and a hollow cylinder are released on a rough, inclined plane. Which of the following will have, maximum acceleration?, (a) Solid cylinder, (b) Solid sphere, (c) Circular disc, (d) Hollow cylinder, 101., If a solid sphere, a disc and a hollow sphere are, allowed to roll down an incline plane from the same, height:, (a) Hollow sphere will reach the bottom first, (b) Disc will reach the bottom first, (c) Sphere will reach the bottom first, (d) All will reach the bottom at the same time, , [Rotational motion], , (d) 10 30m / s, , 106., , In case of a wheel rolling without slipping if, T ,C , and  B represent the linear speeds of a point, at the top, centre and bottom of the wheel, respectively:, (i)  B  0, (ii)  B  C  T, , (iii) T  2C, , (iv) C  B, , (a) (i, iii), , (b) (i, ii, iii), , (c) (ii, iii), , (d) (i, iii, iv), , 107., A solid sphere is rolling on a frictionless surface,, shown in figure with a translational velocity  m/s. If, it is to climb the inclined surface then  should be:, v, , (a) , , 10, gh, 7, , h, , (b)  2gh, , Page 11

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(c) 2gh, , (d), , 108., A disc is rolling the velocity if its center of mass, is Vcm then which one will be correct, , (a) The velocity of highest point is 2 Vcm, and point of contact is zero., (a) The velocity of highest point is V cm and, point of contact is V cm., (b) The velocity of highest point is 2 V cm and, point of contact is V cm., (c) The velocity of highest point is 2 V cm and, point of contact is 2 V cm., 109., A solid cylinder of mass M and radius R rolls, without slipping down an inclined plane of length L, and height h. what is the speed of its centre of mass, when the cylinder reaches its bottom?, (a), , 2gh, , (b), , 3, gh, 4, , (c), , 4, gh, 3, , (d), , 4gh, , 110., A ball rolls without slipping. The radius of, gyration of the ball about an axis passing through its, center of mass is K. if radius of the ball be R, then, the fraction of total energy associated with its, rotational energy will be:, , K R, R2, K2, (c) 2, K  R2, 2, , 2, , 2, , (a), , (b), , K, R2, , (d), , R2, K 2  R2, , 111., A drum of radius R and mass M, rolls down, without slipping along an inclined plane of angle  ., The frictional force:, (a) Decreases the rational and translational, motion, (b) Dissipates energy as heat, (c) Decreases the rational motion, (d) Converts translational energy to rotational, energy, 112., A solid cylinder and a hollow cylinder, both of, the same mass and same external diameter are, released from the same height at the same time on an, inclined plane. Both roll down without slipping., Which one will reach the bottom first?, (a) Both together, (b) Hollow cylinder, (c) Solid cylinder, (d) Both together only when angle of, inclination of plane is 450., 113., The ratio of the acceleration for a solid sphere, (mass ‘m’ and radius ‘R’) rolling down an inclined, plane of angle  ' without slipping and slipping down, the incline without rolling is:, , (a) 5 : 7, (c) 2 : 5, , (b) 2 : 3, (d) 7 : 5, , 114., An inclined plane makes an angle of 300 with the, horizontal. A ring rolling down this inclined plane, , [Rotational motion], , from rest without slipping has linear acceleration, equal to:, (a) 2g/3, (b) g/2, , 10, gh, 7, , (c) g/3, , (d) g/4, , 115., A disc of radius 2m and mass 100 kg rolls o a, horizontal floor. Its center of mass has speed of 20, cm/s. How much work is needed to stop it?, , (a) 3 J, (c) 2 J, , (b) 30 kJ, (d) 1 J, , 116., A solid cylinder of mass 2 kg and radius 50 cm, rolls up an inclined plane of angle inclination 300., The center of mass of cylinder has speed of 4 m/s., the distance travelled by the cylinder on the incline, surface will be:, (Take g = 10 m/s2), (a) 2.2 m, (b) 1.6 m, , (c) 1.2 m, , (d) 2.4 m, , 117., A homogeneous solid cylindrical roller of radius, R and mass M is pulled on a cricket pitch by a, horizontal force. assuming rolling without slipping,, angular acceleration of the cylinder is:, , 3F, 2mR, 2F, (c), 3mR, , F, 3mR, F, (d), 2mR, , (a), , (b), , 118., A string is would around a hollow cylinder of, mass 5 kg and radius 0.5 m. if the string is now, pulled with a horizontal force of 40 N, and the, cylinder is rolling without slipping on a horizontal, surface (see figure), then the angular acceleration of, the cylinder will be (Neglect the mass and thickness, of the string):-, , (b) 16 rad/s2, , (a) 12 rad/s, , (c) 10 rad/s, , 2, , (d) 20 rad/s2, , 119., A solid sphere and solid cylinder of identical, radii approach an incline with the same linear, velocity (see figure). Both roll without slipping all, throughout. The two climb maximum heights hsph and, hcyl on the incline. The ratio, , (a), , 14, 15, , (c) 1, , hsph, hcyl, , is given by:-, , 4, 5, 2, (d), 5, (b), , Miscellaneous Question, 1., , One end of a uniform rod of mass m and length l is, clamped. The rod lies on a smooth horizontal surface, and rotates on it about the clamped end at a uniform, angular velocity  . The force exerted by the clamp, on the rod has a horizontal component, , Page 12

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(a) m  2l, , (b) zero, , (c) mg, , (d), , 1, m 2l, 2, , 2. Point masses m1 and m2 are placed at the opposite, ends of a rigid rod length L, and negligible mass. The, rod is to be set rotating about an axis perpendicular to, it. The position of point P on this rod through which, the axis should pass so that the work required to set, the rod rotating with angular velocity 0 is, minimum, is given by:, , (c) Only the rotational kinetic energy about, the center of mass is conserved, (d) Angular momentum about center of mass, is conserved, 7., A circular platform is mounted on a friction, vertical axle. Its radius R = 2 m and its moment of, inertia about the axle is 200 kgm2. It is initially in, rest. A 50 kg ma stands on the edge of platform and, begins to walk along the edge at speed of 1 ms-1, relative to the ground. Time taken by the man to, complete one revolution is, , (a) 2 s, (c)  s, 8., , m2 L, m1  m2, m, (c) x  1 L, m2, (a) x , , 3., , A tube of length L is filled completely with, an incompressible liquid of mass M and closed at, both the ends. The tube is then rotated in a horizontal, plane about one of its ends with a uniform angular, velocity  . The force exerted by the liquid at the, other ends is:, , (a), , ML 2, 2, , (c) ML 2, 4., , m1 L, m1  m2, m, (d) x  2 L, m1, (b) x , , ML2, 2, ML2 2, (d), 2, (b), , A solid sphere of radius R is placed on smooth, horizontal surface. A horizontal force ‘F’ is applied, at height ‘h’ from the lowest point. For the, ,maximum acceleration of center of mass, which is, correct?, (a) H =R, (b) h = 2R, , (c) h = 0, (d) No relation between h and R, 5., , An automobile moves on a road with a sped of, 54 kmh-1. The radius of its wheels is 0.45m and the, moment of inertia of the wheel about its axis of, rotation is 3 kg m2. If the vehicle is brought to rest in, 15 s, the magnitude of average torque transmitted by, its brakes to wheel is:, (a) 2.86 kg m2s-2, (b) 6.66 kg m2 s-2, , (c) 8.58 kg m2 s-2, 6., , (d) 10.86 kg m2 s-2, , A solid homogeneous sphere is moving on a, rough horizontal surface, partly rolling and party, sliding. During this kind of motion of the sphere:, (a) Total kinetic energy of the sphere:, (b) Angular momentum of the sphere about, the point of contact with the plane is, conserved, , , , s, 2, 3, (d), s, 2, , Two discs of same moment of inertia, rotating about their regular axis passing, through center and perpendicular to the plane, of disc with angular velocities 1 and 2 ., They are brought into contact face to face, coinciding the axis of rotation. The expression, for loss of energy during this process is:-, , 1, I (1  2 ) 2 (b) I (1  2 )2, 4, 1, 1, (c) (1  2 )2, (d) I(1  2 ) 2, 8, 2, [(a), , 9., , Three objects, A : (a solid sphere), B: (a thin, circular disk) and C: (A circular ring), each have the, same mass M and radius R. They all spin with the, same angular speed  about their own symmetry, axes. The amounts of work (W) required to bring, them to rest, would satisfy the relation, (a) WB > WA > WC, (b) WA > WB > WC, (c) WC > WB > WA, (d) WA > WC > WB, 10., A solid sphere is rotating freely about symmetry, axis in free space. The radius of the sphere is, increased keeping its mass same. Which of the, following physical quantities would remain constant, for the sphere?, (a) Rotational kinetic energy, (b) Moment of inertia, (c) Angular velocity, (d) Angular momentum, 11., A solid sphere is in rolling motion. In rolling, motion a body possesses translational kinetic energy, (Kt)as well as rotational kinetic energy (Kr), simultaneously. The ratio Kt : (Kt + Kr) for the sphere, is, (a) 10 : 7, (b) 5 : 7, , (c) 7 : 10, 12., , (d) 2 : 5, , Moment of inertia of a body about a given, axis is 1.5 kg m2. Initially the body is at rest. In order, to produce a rotational kinetic energy of 1200 J, the, angular acceleration of 20 rad/s2 must be applied, about the axis for a duration of :-, , (a) 2 s, [Rotational motion], , (b), , (b) 5s, Page 13

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(c) 2.5 s, 13., , (d) 3 s, , A metal coin of mass 5 g and radius 1 cm is, fixed to a thin stick AB of negligible mass as shown, in the figure. The system is initially at rest. The, constant torque, that will make the system rotate, about AB at 25 rotations per second in 5 s, is close to, , (a) 4.0  10 6 Nm, (c) 1.6 105 Nm, , (b) 2.0  10 5 Nm, (d) 7.9  106 Nm, , ...By Praveen Gupta, , [Rotational motion], , Page 14