Last Leap for NEET 2020 PDF

https://neetforsure.blogspot.com/ https://neetforsure.blogspot.com/ !"#$%#$& S. NO. PARTICULARS PAGE NO. 1. Preface...........................................................................................

https://neetforsure.blogspot.com/ https://neetforsure.blogspot.com/ !"#$%#$& S. NO. PARTICULARS PAGE NO. 1. Preface................................................................................................. (i) – (i) 2. Physics................................................................................................. 01 – 80 3. Zoology.............................................................................................. 81 – 260 4. Answers........................................................................................... 261 – 273 https://neetforsure.blogspot.com/ https://neetforsure.blogspot.com/  Preface Dear NEET Aspirants, I am pleased to release this package “Last Leap” for NEET 2020. This package contains selected and important questions which has been prepared and compiled by our expert faculties who have been teaching AIPMT/NEET since decades. This package is available in 2 parts viz. Part (I) and Part (II). When a student will try to solve these questions, he/she can have a real feel of the examination. These questions will open the different layers of the brain and will stimulate the deepest nervous tissue to think and recall as well as analyze the trick in the questions. I am very confident that if a student sincerely solves these questions independently, there is no reason why he/she cannot be among the top rankers in the country in the NEET. The “Last Leap” is going to be the winning Leap for every student who puts his heart and mind on the questions given in this package. Wishing you a brighter career. J.C. CHAUDHRY Chairman Aakash Educational Services Limited (i) https://neetforsure.blogspot.com/ https://neetforsure.blogspot.com/  PHYSICS CHAPTER No. TOPIC PAGE No. 1. System of Particles and Rotational Motion............................... 01 – 26 2. Current Electricity....................................................................... 27 – 46 3. Semiconductors......................................................................... 47 – 58 4. Dual Nature of Radiation and Matter......................................... 59 – 64 5. Ray Optics and Optical Instruments......................................... 65 – 80 https://neetforsure.blogspot.com/ https://neetforsure.blogspot.com/ Chapter 1 System of Particles and Rotational Motion SECTION - A (1) ! ! ! (2) g (3) #" (4) Zero Objective Type Questions 5. A solid sphere mass M and radius R is in pure 1. If a body is moving in a circular path with rolling with angular speed on a horizontal plane decreasing speed, then (symbols have their usual as shown. The magnitude of angular momentum of meaning) ! "! ! ! sphere about origin O is (1) ! ! " (2) !! " ! ! " (3) ! ! " " (4) All of these 2. A particle of mass m1 moving with certain velocity hits a sphere of mass m2 at rest elastically such ! that initial velocity of particle is not along the line joining their centre of mass. If their final velocities $ # are normal to each other, then ! ! (1) m1 = m2 (2) m1 = 2m2 (1) !" ! (2) !" ! " " (3) 2m1 = m2 (4) m1 > > m2 3. Three thin identical rods of mass ‘M’ and length ‘L’ ! ! (3) !" ! (4) !" ! each are connected to form a shape as shown in " " figure. The moment of inertia of this arrangement 6. Two particles of mass 2 kg and 4 kg are projected about an axis YY is from the top of a tower simultaneously such that ! 2 kg is with speed 20 m/s at an angle 30° above horizontal and 4 kg is with 40 m/s horizontally. Acceleration of the centre of mass of the system of two particles is ! ! (1) (2) ! " !" (3) g (4) 2g !" ! !"! (1) (2) 7. Moment of inertia of a uniform disc of mass M and ! ! radius R about an axis passing through its edge ! !"! !" and perpendicular to its plane is I. Its moment of (3) (4) inertia about its diameter will be " ! 4. Three masses m, 2m and 3m are thrown from the ! top of a tower such that m is thrown vertically (1) I (2) upward with 10 m/s, 2m is thrown horizontally with ! 15 m/s and 3m is thrown vertically downward with ! ! 5 m/s. The acceleration of centre of mass of three (3) (4) body system will be " ! Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/  2 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 8. A uniform rod of mass 2 kg and length 1 m is free to 12. Two particles of masses 2 kg and 3 kg start to rotate in a vertical plane about a fixed horizontal axis move towards each other due to mutual forces of through one end. The rod begins rotating from rest attraction. The speed of first particle is v1 and that from its unstable equilibrium position. Its angular of the other is v2 at a certain instant. The speed acceleration, when it has turned through an angle of of centre of mass is 30° is "! " " !!! "! " (1) (2) !! ! # (1) g rad/s2 (2) rad/s2 " !!! "! " (3) (4) Zero !! !! # (3) rad/s2 (4) rad/s2 " # 13. An electric fan rotating at 1200 rpm is switched off. 9. In figure, a sphere rolls without slipping on a plank If the fan stops after 10 seconds, the number of moving with velocity V0. The radius and angular revolutions completed by the fan before it stops is velocity of the spheres are r and respectively. The (assume uniform retardation) velocity of centre of mass Vcm of the sphere w.r.t. (1) 100 (2) 50 ground is (3) 40 (4) 20 !!" 14. What is the moment of inertia of a solid sphere of mass m and radius R kept with its centre as x-axis !! at (2R, 0) about y-axis? !! !! (1) !" ! (2) !" ! " " (1) V0 + r (2) V0 – r ! ! (3) r (4) V0 (3) !" ! (4) !" ! " " 10. A disc rolls without slipping and climbs on a rough incline and comes back. During the motion on the 15. A solid sphere is rolling without slipping such that incline velocity of its centre of mass is v. Ratio of speed of points at horizontal extreme points A and B is # ! " $% (1) Friction is downward during upward journey (2) Friction is upward during upward journey (1) 1 : 1 (3) Friction is zero (2) ! #$ (4) Information is insufficient to predict 11. Moment of inertia of a uniform rod of length L and (3) 2 : 1 mass m about an axis through one end at an angle 45° to rod is (4) $# ! 16. A ring and a solid cylinder both are allowed to roll !"! (1) down without slipping from a certain height on an ! incline simultaneously. If time taken to reach the !"! bottom by them are t1 and t2 respectively, then (2) ! (1) t1 < t2 ! !" (2) t1 > t2 (3) !" (3) t1 = t2 ! !" (4) Relation between t1 and t2 depends on their (4) # masses Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 3 17. A particle of mass m moves along the line y = x, (1) Horizontally towards right with speed v. The magnitude of angular momentum (2) Vertically upward about the point ! "!# $% is (3) Vertically downward (1) !!"# (2) 2mva (4) Zero !"# 23. Three rods each of mass m and length l are joined (3) mva (4) ! together in the form of an equilateral triangle as shown. The moment of inertia about an axis along 18. A solid sphere of mass m and radius R released median of the triangle from the top of an inclined plane such that it rolls down without slipping. If the coefficient of friction is and angle of inclination is with horizontal, then force of friction acting on the body is (1) !" !"# (2) !" !"# ! ! !" !" (1) (2) ! ! #$ #$% !#! %&' (3) (4) ! " & ( !" !# (3) (4) " ) 19. Two spherical bodies of equal mass (M) revolve about their centre of mass. The distance between 24. A ring of mass M and radius R is rolling with the centre of the two masses is r. The angular angular speed on a horizontal plane as shown in momentum of each about their centre of mass is the figure. The magnitude of angular momentum of the ring about origin O is $ ! (1) ! !" ! # (2) $% & ! ! ! ! ! ! !" # (3) "!" # (4) " " " ! 20. Two identical particles are projected simultaneously (1) MR2 ! from a tower with speeds v and at an angle 30° (2) 2MR2 ! and 60° simultaneously. The acceleration of centre ! of mass of the balls is (3) MR 2 # ! ! (1) (2) ) ! # (4) MR 2 ! ! (3) (4) g * 25. Force is applied tangentially on the topmost point of ring kept on a rough horizontal surface such 21. Centre of mass of a system of particles that rolls without slipping. Force of friction acting on (1) Depends on frame of reference it, is (2) Does not depend on frame of reference ! (3) May change due to internal forces (4) All of these 22. A ring is rolling without slipping on a horizontal (1) Horizontally backward plane with velocity v and acceleration a. The (2) Horizontally forward acceleration of point of contact is (3) May be horizontally forward or backward ! (4) Zero Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/  4 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 26. A solid sphere is given a sharp impulse at D on a !" (1) mR2 (2) !" ! rough horizontal surface as shown in the figure. # Before it starts pure rolling its angular momentum ! can be conserved about (3) !" ! (4) 3mR2 " # % 32. A boy is standing on a disc rotating about the $ " vertical axis passing through its centre. He pulls ! !"#$% his arms towards himself reducing his moment of (1) A (2) B inertia by a factor m. The new angular speed of the disc becomes double of its initial value. If (3) C (4) O moment of inertia of the boy is I0 then moment of 27. A disc rolls on ground without slipping. Velocity of inertia of the disc will be centre of mass is v. The speed of particle P at circumference (vp) is ! !" (1) 2I0/m (2) !! # " $ " % "& ! ! !! " !"#$ ! "" (3) !! # " $ (4) # $ % "& % !" & (1) v (2) !! 33. What is the shape of the graph between the (3) 2v (4) "! angular momentum and rotational kinetic energy of a rigid body about a given axis? 28. Total kinetic energy of a solid sphere of mass 1 kg rolling with velocity 1 m/s is (1) Straight line (2) Hyperbola ! $ (3) Parabola (4) Exponential (1) " (2) % # " 34. Four masses are joined to a light circular frames " ! in the figure. The radius of gyration of this system (3) # (4) % about an axis passing through the centre of the $% & circular frame and perpendicular to its plane would 29. The moment of inertia of a uniform semicircular be (where a is the radius of the circle) disc of mass M and radius R about axis through centre of mass on to its plane as shown in " figure is "! !! !! " ! !"# ! " ! ! !" !" # ! (1) (2) (1) (2) ! ! ! ! ! ! !" !" (3) (4) (3) a (4) 2a ! !"# 30. When a planet revolves around the sun in an 35. Five particles of mass 2 kg each are attached to the circumference of circular disc of a radius 0.1 elliptical orbit then which of the following remains m and negligible mass. Moment of inertia of the constant? system about the axis passing through the centre (1) Velocity (2) Angular velocity of disc and perpendicular to its plane is (3) Areal velocity (4) Both (2) & (3) (1) 1 kg m2 (2) 0.1 kg m2 31. From a circular disc of radius R and mass 4m, a (3) 2 kg m2 (4) 0.2 kg m2 ! small disc of radius is removed concentrically. 36. A ring of mass M and radius R is rolling with ! The moment of inertia of the remaining disc about angular speed on a horizontal plane as shown in an axis perpendicular to the plane of the disc and the figure. The angular momentum of the disc passing through its centre is about point P is Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 5 $ # ! # ! (1) " (2) " $ % ! ! # !" ! " (3) (4) MR2 ! ! " ! 41. A thin uniform rod has moment of inertia I about an !" (1) MR2 (2) axis parallel to its length at a certain distance. If ! on heating its length increases by 2%, then (3) 2MR2 (4) ! moment of inertia of rod will change by ! !" (1) 0 % (2) 1 % 37. A thin wire of length l and uniform linear mass ! density is bent in the form of a square. Its (3) " (4) 4 % moment of inertia about an axis along one of its # edge is 42. The radius of gyration of a ring of radius r about an axis along one of its diameter is ! ! ! !!" " !!" ! (1) # $ (2) # $ (1) r (2) " % #& ! % #& ! ! ! " ! !!" ! !!" (3) !" (4) (3) # $ (4) # $ ! " % #& " % #& 43. A uniform rod of mass M and length L is free to 38. A disc of mass M and radius R starts falling down rotate about one of its ends in a vertical plane. If as shown in the figure. The string unwinds without it is released from a horizontal position, then what slipping on the disc. The instantaneous power will be tangential acceleration of its centre of mass developed by the tension is when it becomes vertical? ) (1) Zero (2)! ! ! $ & (3) (4) $ # $ $ 44. A solid sphere slides from top to bottom of a "!" smooth inclined plane. It takes time T. If it rolls on a rough inclined plane of same dimensions, then $ % time taken by it to reach from top to bottom will be (1) T × R (2) ! " (3) 2T × R (4) Zero (1) !! (2) # # 39. Two particle of mass m and 4m are initially at # % rest. They start moving towards each other due to (3) # (4) # their mutual gravitational attraction. At an instant $ # 45. A particle of mass M revolves in a circular path of velocity of mass m is !"!" the velocity of mass 4m radius R with constant angular momentum L. The at that instant is linear momentum of particle is (1) Zero (2) " !! ' " (1) (2) %( ! ! ! (3) " (4) "! "! ! ! %( " (3) ! (4) 40. A section of mass M and radius R is cut from a "# ' uniform circular disc. Its moment of inertia about 46. A ball of mass m and radius r is tied to a string an axis AA passing through its centre of length L. If it revolves in a horizontal circle with perpendicular to its plane is constant angular speed , then the magnitude of ! torque acting on it is !"# !"#$ (1) Zero (2) $ ! !" ! " !" ! (3) # #$ (4) # # $ $ $ !" % & Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/  6 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 47. A uniform thin rod of mass 4 kg and length 8 m is 52. The moment of inertia of a horizontal ring about its folded to form a circular ring, then the moment of vertical axis through centre is mR2. Moment of inertia (in kg m2) of ring about one of its diameter inertia about its tangent parallel to the plane is will be ! ! ! "# !!" #( (1) (2) (1) ! (2) ! " " ! ! $% !" #( !!" (3) ! (4) ! (3) (4) ! " 48. A particle is moving on a circular path with 53. The ratio of total energy to the rotational kinetic continuously decreasing speed. The correct energy of rolling solid sphere is relation is [where symbols have their usual meanings] ! ! (1) (2) ! "! "! ! " # (1) ! ! " (2) " !! " "! ! " $ (3) # !! (4) All of these (3) (4) " # ! 49. During the motion of a planet around the sun, ! "# which of the following physical quantity remains 54. The rotational analogue of equation $ is "% conserved (1) Moment of inertia of planet about sun #$ ! (1) (2) " #% !# (2) Angular velocity of planet about sun !" !" "! (3) Angular momentum of planet about sun (3) " ! (4) ! !# "# "# (4) All of these 55. A mass of 2 kg is moving on a circular path of 50. The ball is rolling without slipping as shown in radius 2 m at 30 revolution per minute. The kinetic figure, then it reaches to the height of (no loss of energy of the mass (in joule) is energy in the bend) (1) 2 (2) 2 2 $% ## !" (3) 4 2 ! "#$#!"#$%& '"( (4) 8 2 (1) 10 m (2) 5 m 56. The angular frequency of small oscillations of the given rod about O (mass m, length l) is (3) 2 m (4) 20 m " 51. Which of the following graphs closely represents the variation in kinetic energy of a planet as it moves once round the sun in its elliptical orbit? (t : time) ! # !" !" (1) (2) ! ! !" !" ) ! !! (1) (2) ! !) "" (3) (4) #! !! (3) (4) ! ! !" "" Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 7 57. Moment of inertia of a non-uniform ring of mass M ! !" and radius R about axis through centre and normal (1) ml2 (2) ! to its plane I is ! ! !" !" (1) I > MR2 (3) (4) ! " (2) I < MR2 62. Which of the following is/are axial vector? (3) I = MR2 (1) Angular momentum (4) I MR2 (2) Torque 58. Angular velocity and angular momentum (3) Angular velocity (1) Both are axial vectors (2) Both are scalar (4) All of these (3) Only angular momentum is vector 63. A man throws a rotating disc of mass m in upward direction. The velocity of centre of mass of disc is (4) Both may be linear vectors 20 m/s. If disc is rotating about its axis 59. In the case of rolling with backward slipping friction perpendicular to the plane and axis is horizontal, then the time after which its velocity of centre of (1) Opposes the rotational motion and support the mass becomes equal and opposite to the initial is translational motion (neglect air friction, g = 10 m/s2) (2) Opposes both translational and rotational (1) 4 s motion (2) Less than 4 s (3) Supports only the rotational motion (3) Greater than 4 s (4) Supports both the motions (4) Less or greater than 4 s depend on the 60. A disc is set into pure rolling on an inclined plane. direction of angular velocity of disc Let us taken three points on the disc as shown in 64. A disc is rolling with slipping on a horizontal figure. Then vB : vC : vD is (vB, vC and vD are surface then the ratio of its total kinetic energy to corresponding speeds) rotational energy is (assume angular velocity remains constant) # (1) 3 " (2) Greater than 3 $ ! (3) Less than 3 (4) May be greater or less than 3 65. A solid sphere is rolling up on an incline. If it is thrown in upward direction with some initial angular velocity and its motion is pure rolling, then its (1) 1 : 1 : 1 (2) $# ! # ! angular momentum about the initial point of contact during its upward motion (3) ! # $# ! (4) !" # " # (1) Remains constant 61. If all the three rods AB, AC and AD are of same (2) Increases mass m and length l, then the moment of inertia of system about the given axis OO on their plane (3) Decreases is (4) Increases or decreases depend on the value of " friction ! 66. Angle between angular velocity and acceleration of !"# a particle in uniform circular motion is (1) Zero (2) 60° # $ % !’ (3) 120° (4) 90° Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/  8 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 67. Two masses m and 2m are at a distance r and if 73. A rod is held vertically on a smooth horizontal they revolve due to their mutual attraction then the surface. If it is slightly disturbed, then the path ratio of their angular velocities and the linear followed by the centre of mass of the rod is velocities respectively are (1) Circular (2) Elliptical (1) 1 : 1, 1 : 1 (2) 2 : 1, 1 : 1 (3) Straight line (4) Parabolic (3) 1 : 1, 2 : 1 (4) 1 : 1, 1 : 2 74. A quarter ring having radius R is placed as shown 68. If mass of sun and earth suddenly reduced to half in figure. The co-ordinates of the centre of mass are and orbit remains same then which of the following will be changed? (1) Angular velocity of earth about sun (2) Rotation speed of earth about its axis ! (3) Angular momentum (4) All of these !"#! ! ! ! ! ! 69. Let $ " $ !"# ! represent angular velocity, linear & !! !! # velocity, angular acceleration, and linear (1) (0, 0) (2) $ " ! % " acceleration of a particle respectively, moving on a circle. Choose the incorrect option &! ! # &! ! # (3) $ ! ! (4) $ ! ! (1) ! may be constant % " %" "" ! 75. Two point masses 6 kg and 3 kg are fixed at two (2) ! must be variable ends of a light rigid rod having length of 2 m. The ! moment of inertia of the system about the centre of (3) ! cannot be zero ! ! mass and perpendicular to the length of the rod is (4) ! cannot be negative 70. The centre of mass of a body does not coincide with centre of gravity in the case of (1) A ring !" #$%& ! '$%& (2) An irregular shaped rigid body (3) A mountain (4) A solid hemisphere (1) 2 kg m2 71. Two particles having mass ratio 1 : 2 are moving (2) 4 kg m2 towards each other with same speed v0. The speed (3) 8 kg m2 of their centre of mass is (4) 16 kg m2 !! (1) Zero (2) 76. Three identical rods each having mass m and length ! l are fixed in the form of an equilateral triangle. The "! ! moment of inertia of the system about the vertex (3) (4) v0 and perpendicular to the plane of the triangle is ! 72. Two bodies A and B are released from distance 5a. !" ! The masses of the bodies are 2m and 3m (1) ! respectively. If these are moving due to mutual attraction then the distance covered by the body A "!" ! (2) before collision is ! "" #" !" ! (3) !! !" (1) 3a (2) 2a !" ! (4) (3) 5a (4) a ! Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 9 77. A square plate is having mass m and dimension a. 80. A cubical block of mass m and side a rests on a Find the moment of inertia about the axis passing rough inclined plane making an angle with the through the centre and in the plane of the plate as shown in the figure. horizontal. The torque of reaction force about the centre of mass of the block is !"# "#$ (1) ! ! (2) amg sin (3) 2amg sin ! !"# "#$ (4) ! #* ! !" ! 81. A ring of mass m and radius R is rolling without (1) %&' ! (2) !"#! * $% slipping with speed of the centre v, on a horizontal surface. The ring collides elastically with a smooth !" ! #$ ! (3) (4) vertical wall. The angular momentum of the ring just !" $ after collision about the point of contact on the 78. The moment of inertia of an incomplete disc of horizontal surface, is mass M and radius R as shown in figure about the (1) mvR (2) 2 mvR axis passing through the centre and perpendicular (3) 3 mvR (4) Zero to the plane of the disc is 82. The coefficient of friction between a solid cylinder !"# and a rough inclined plane is just sufficient for pure rolling of the cylinder. Which of the following bodies can move with pure rolling on the inclined plane? $ ! (1) Hollow cylinder (2) Solid sphere (3) Hollow sphere (4) Ring !" ! #!" ! 83. A hollow sphere having mass m and radius R, is (1) (2) ! "! moving as shown in the figure. If the speed of (%( ! &#$ ! centre of mass of sphere is v0 and angular speed (3) (4) "" * $% is ". The angular momentum of the sphere ( 79. A uniform rod having length l is hinged at one end about point O is and is free to rotate in vertical plane. The rod is released from the position making angle with the vertical. The acceleration of the free end of the rod ! at the instant it was released is "! ! " (1) "# ! ! ! (2) mv0R %! "#$ %! "#$ !# " " (1) (2) ! ! (3) # %! "#$ %! "#$ (3) (4) "# ! ! & & (4) ! Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ 10 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 84. On a rough horizontal surface, a cubical block of side a and mass m is projected horizontally. The torque on the block about its centre of mass till the ! block stops is equal to " (1) Zero (2) $%& ! (3) mga (4) mga 85. A ladder of length l and negligible weight leans !" "! against a smooth wall at an angle with the (1) (2) ! % horizontal. If is the coefficient of friction at the bottom, then the maximum distance from the ! ! (3) (4) contact point upto which a person can climb before ( !( the ladder slips, is 89. A hollow sphere is in pure rolling on a horizontal (1) l tan surface. The fraction of translational kinetic energy is (2) l cos " " (1) (2) (3) l sin ! ! (4) l cot ! $ (3) (4) 86. An insect initially on the circumference of a disc, starts # # moving along a chord of the disc, rotating about an 90. A hollow sphere and a solid sphere are released on axis passing through the centre and perpendicular to a rough inclined plane. Assume no slipping the plane of the disc. Its angular speed between the spheres and the plane. If v1 and v2 is (1) Increases the velocity of centre of mass at the bottom position respectively then (2) Decreases (3) First increases than decreases (1) v1 > v2 (2) v1 < v2 (4) First decreases than increases (3) v1 = v2 (4) v1 = 2v2 87. Two discs A and B are rotating about parallel axes 91. A particle is moving along path AB. The angular passing through their centres P and Q and momentum of particle about the origin perpendicular to the plane of discs. If there is no slipping at the contact point then # # ! $ " " % ! !# (1) Remains the same (2) First increases then decreases (1) Angular speed of A and B are same (3) First decreases then increases (2) Angular speed of A is more than that of B (4) Is zero (3) Angular speed of A is less than that of B 92. Which of the following quantities is a vector? (4) Angular speed of A is half of angular speed of B (1) Angular displacement for complete circle 88. A ring is free to move in vertical plane about an axis passing through the circumference and (2) Average angular velocity perpendicular to its plane. When it is released from (3) Moment of inertia top most position, the angular speed of the centre of mass of the ring at the lowest position is (4) A very small angular displacement Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 11 93. The moment of inertia of a uniform cylinder of radius 98. A thin rod of length l and mass m is bent at 90° R, mass M and length L about an axis passing at its mid point (see diagram). The moment of through its centre of mass and perpendicular to its inertia about the axis AB is length is !#! !" ! !#! !" ! !"# (1) (2) "# ! "# ! #%! #$ ! (3) (4) $% ' $ % 94. For a rigid body rotating about a fixed axis, which # $ of the following quantities is same at an instant for (1) !" ! (2) #) ! all the particles of the body? !" $! (1) Angular acceleration $ ! " ! (3) !" (4) !" # ! (2) Angular velocity 99. A rigid body is rolling without slipping, if the ratio (3) Angular displacement in the given time interval of translational kinetic energy and rotational kinetic (4) All of these energy is 2 : 1, the body may be 95. Three identical thin rods of each of mass m and (1) A solid sphere length l form an equilateral triangle ABC as shown in the diagram. The moment of inertia of the (2) A ring system about the axis AB is (3) A hollow cylinder ! (4) A solid cylinder 100. A ring of radius 0.25 metre and mass 10 kg is rotating about its diameter with angular speed 40 rad/s. Its kinetic energy is " # (1) 5 J (2) 50 J " ! (3) 250 J (4) 500 J (1) ml2 (2) !" ! 101. A projectile of mass 1 kg is projected with initial velocity 20 m/s at an angle 60° with horizontal. The " ! " ! (3) !" (4) !" angular momentum of the projectile about point of ! ! projection, when it is at maximum height is 96. A particle of mass 1 kg initially at rest at the origin (1) 82 kg m2s–1 explodes into two fragments of mass 400 g and 600 g. At a certain instant the x–coordinate of the (2) 120 kg m2s–1 bigger fragment is 12 cm, then x–coordinate of the smaller fragment will be (3) 75 kg m2s–1 (1) –18 cm (2) – 12 cm (4) 150 kg m2s–1 (3) –8 cm (4) –4 cm 102. A light and flexible string can support maximum tension 40 N. A stone of mass 0.5 kg tied to one 97. An electric fan running at a speed of 60 rpm, is end of string is revolving in a vertical circle of radius switched off at t = 0. If the fan stops after 1m. The maximum value of angular velocity of 10 seconds, the number of revolutions made by stone can be [Take g = 10 m/s2] the fan till it stops is (assume uniform retardation) (1) 6.6 rad/s (1) 10 (2) 5 (2) 9.5 rad/s (3) 2.5 (3) 11.5 rad/s (4) 1 (4) 8.4 rad/s Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ 12 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 103. Four identical particles each of mass 1 kg are 108. If a constant torque of 500 Nm turns a wheel of placed at the corners of a square of side 2 m. If moment of inertia 100 kgm2 about an axis passing this system of particles is rotated about the through its centre, then the gain in angular velocity diagonal AC then moment of inertia of the system in 2 s is will be (1) 10 rad/s (2) 5 rad/s ! " (3) 20 rad/s (4) 25 rad/s 109. The torque of force F about origin O is %')'$'* ! -&'+'*-'((', ! $ # ) !"# (1) 4 kg m2 (2) 8 kg m2 $%&'%( (3) " ! kg m2 (4) 16 kg m2 104. A solid sphere, a disc, and a cylinder are kept on " the top of a smooth inclined plane. If they are # $ allowed to fall along inclined plane, then ! ! (1) "#$ %&!! Nm (2) "#$ %& !! Nm (1) Disc reach bottom first ! ! (3) "# $ %&!! Nm (4) " !! Nm (2) Solid sphere reach bottom first 110. A particle of mass m is moving on x-y plane with (3) All reach bottom together constant velocity in a circle of radius R as shown (4) Only disc and cylinder reach bottom together in figure. Then its angular momentum is maximum 105. If a solid sphere is rolling without slipping and its about z-axis for its position at total kinetic energy is 280 J, then its translational ! kinetic energy will be ( & ( (1) 80 J (2) 175 J ' % (3) 200 J (4) 280 J 106. A body of mass M is moving on a circular track of !"#$#% ( ( $ radius r in such a way that its kinetic energy k " !##$"% depends on the distance travelled by the body s according to relation k = s, where is a (1) B (2) C constant. The angular acceleration of the particle is (3) A (4) Both (1) & (2) ! ! 111. Which of the following quantities is conserved (1) ! (2) when the torque acting on a system is zero? " " (1) Kinetic energy !" ! (3) (4) %& (2) Linear momentum 107. A particle moves in a circle with constant angular (3) Rotational kinetic energy speed ( ) about point O. Then angular speed about point A will be (4) Angular momentum 112. Two small balls A & B of mass mA and mB are attached rigidly to the ends of a light rod of length d. The structure rotates about the # ! perpendicular bisector of the rod at an angular " speed. The angular momentum of the system about the axis of rotation is ! (1) 2 (2) !! ! (1) +#! #" , (2) !"! "" " + # !! !" (3) (4) (3) mA d2 + mB d2 (4) " &! &! Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 13 113. A uniform solid sphere of mass m = 100 g rolls 117. Four thin rods each of mass m and length L form without slipping on a plane surface so that its a square. The moment of inertia about any side of centre moves at a speed of 2 cm/s. the square is Its total kinetic energy is !!"" (1) 5.6 × 10–5 J (2) 2.8 × 10–5 J (3) 2 × 10–5 J (4) 1.4 × 10–5 J !!"" !!"" 114. If mA = 40 kg, mB = 30 kg, mC = 20 kg, mD = 10 kg masses are placed at the corners of a !!"" square of length 1 unit, then the coordinates of ! centre of mass is (1) !"! (2) 4 mL2 " " !"! # & % (3) (4) !#! ! ! 118. Two bodies A & B made of same material have the moment of inertia in the ratio IA : IB = 16 : 18. # $ The ratio of their masses mA : mB is given by ! !"#$"% (1) 1 : 1 (1) (0.5, 0.3) (2) (5, 3) (2) 2 : 3 (3) (0.3, 0.5) (4) (0, 0) (3) 8 : 9 115. A disc is performing pure rolling with constant (4) Can’t be uniquely determined angular velocity on a smooth stationary surface. 119. A circular disc of radius R is rotating about its axis Then at any instant for point of contact P of the normally through centre O with uniform angular disc velocity. The maximum magnitude of relative velocity of point A relative to point B on the disc is ! # ! # " $ (1) Velocity is v, acceleration is zero " !! (2) Velocity is zero, acceleration is (1) R " (3) Velocity is zero, acceleration is zero (2) Zero ! (3) 2R ! (4) Velocity is v, acceleration is " (4) )( 116. A wheel of moment of inertia I and radius R is ! rotating about its axis at an angular speed 0. It 120. A force ! "#"! $ #! %$! & ' is acting at point picks up a stationary particle of mass m at its (2 m, –3 m, 6 m). Find torque of this force about edge. The new angular speed of the wheel is a point whose position vector is "#!! $ "! %#! & m ! ! (1) ! "# " (1) " #$!! % "! &#! ' Nm ! ! (2) (2) " #$!! % "! &#! ' Nm ! (3) ! 0 (3) "#$!! % "! &#! ' Nm ! ! ! (4) (4) #'"! $" #! $(!! & Nm ! "# " Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ 14 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 121. From a uniform circular plate of radius 2R, a disk 124. Three identical cubes each of mass 1 kg are kept of radius R has been removed. Then centre of as shown in figure touching each other, with their mass of remaining plate is at xcm equal to centres on a straight line. If their centres are " marked P, Q, R respectively, the distance of centre of mass of the system from P is !! ! " # # ! $% $# %# !" "# !# !!" (1) (2) " ! !" !# $% %# (3) (4) ! " 125. A planet moves around the sun. It is closest to the $ ! sun at distance d1 and has velocity v1. Its velocity (1) (2) v2 at farthest distance d2 will be % ! ! !# !! !! (3) (4) (1) "! (2) "" ! " !" !" 122. In the three figures, each wire has mass M, radius + !! +#! R and has uniform mass distribution. If they form (3) "# (4) "# part of a circle of radius R then about an axis +#! + !! perpendicular to the plane and passing through the 126. If a satellite is orbiting in elliptical orbit then the centre (shown by crosses), their moment of inertia quantity which does not remain constant is is in the order (1) Areal velocity (2) Angular momentum (3) Linear momentum (4) Total energy ! ! 127. If " is velocity of a planet when its position vector ! ! from the sun is ! , then its areal velocity is !"# !"# ! ! ! ! ! (1) - & "- (2) "! " " ! # ! ! ! ! (3) ! " ! " " (4) ! " ! " " !"# 128. Rotational kinetic energy, angular momentum and (1) IA > IB > IC moment of inertia of a body about a given axis are E, L and I respectively. If [E x L y I z ] is (2) IA = IB = IC dimensionless, then x, y and z are respectively (3) IA < IB < IC (1) [1, 2, 1] (2) [1, –2, 1] (4) IA < IC < IB (3) [–1, 2, 1] (4) [1, 1, 1] 123. A solid body rotates about a stationary axis ! ! ! according to the equation, = 6t – 2t3. What is 129. If ! ! " and are radius vector, velocity and angular the average angular velocity over the time interval velocity of a particle executing circular motion, between t = 0 and the time when the body comes then which of the following relations is correct? to rest? ( : angular displacement, t : time) ! ! (1) ! " ! (1) 1 rad/s ! ! ! (2) ! " (2) 2 rad/s ! ! ! (3) 3 rad/s (3) ! !" (4) 4 rad/s ! (4) " ! ! ! Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 15 130. A ring of mass m and radius R is rotating with 135. A solid sphere is set into pure rolling on an angular velocity about its diameter. Rotational inclined plane. Speed of centre C, when the sphere kinetic energy of the ring is reaches the bottom, will be ! ! (1) !" ! ! (2) #$ ! ! " $ ! " (3) !" ! ! (4) mR2 2 " ! 131. A solid sphere is released from the top of an inclined plane as shown in figure. If it is rolling without slipping, then force of friction acting on the sphere is !"!".!, (1) (2) # ( $"!" "/!, (3) (4) # ( (1) Up the plane (2) Down the plane 136. A tangential force F acts at the top of a thin spherical shell of mass m and radius R. The (3) Zero (4) Normal to the plane acceleration of the shell, if it rolls without 132. A disc of mass m and radius R is rolling without slipping, is slipping on a horizontal floor such that velocity of its centre of mass is v. Its angular momentum " about instantaneous axis of rotation is ! !!"# (1) mvR (2) " ! "# (1) (2) #"$ #!"# " #$ (3) (4) ! " !! !! (3) (4) 133. Maximum and minimum distance of a planet from "" "" sun are in ratio 4 : 3. Ratio of maximum to 137. A solid cylinder of mass m and radius r is rotating minimum speed of the planet in its elliptical orbit is about its axis with a constant angular speed. If (1) 16 : 9 (2) 7 : 1 speed of a particle at circumference is v, then the rotational kinetic energy of the cylinder is (3) 4 : 3 (4) 49 : 1 134. Moment of inertia of a thin uniform rod of length l and mass m about an axis passing through a ! ! point at a distance of from centre O and at an ! angle of 60° to the rod is " ! !"# " ! ! ! (1) !" ! " ! !!" ! !" ! (2) !" ! (1) (2) # "# ! $ (3) !" ! !" ! !" ! " (3) (4) ! !" (4) mv2 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ 16 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 138. A ring of radius r has its mass non-uniformly 144. A planet of mass m moves around the sun of distributed over its circumference with centre at the mass M in an elliptical orbit. The maximum and origin. If x is the distance of centre of mass of the minimum distances of the planet from the sun are ring from its centre, then r1 and r2 respectively. The time period of the planet (1) x = r (2) x < r is proportional to (3) x > r (4) ! ! " (1) !$!"# (2) !#!"# 139. If a wheel starts rotating with constant angular (3) !!$ !# " !"# (4) !!$ !# " !"# acceleration, it completes angle 1 in first 2 s and 145. A disc of radius R is moving without slipping with ! in next 2 s it rotates through angle 2. Here a linear velocity v. If vP and vQ are velocities of " is equal to points P and Q respectively as shown in figure, (1) 1 (2) 2 ! !! ! then the ratio is ! !" ! (3) 3 (4) 4 !"#$%&'()*"+' 140. A solid sphere is rotating about a diameter, then # (1) All the particles have same linear speed " ! (2) Different particles have different angular speed (3) The particles on the diameter have no linear acceleration (1) 2 (2) ! (4) Particles on the surface have no linear acceleration ! (3) (4) 1 " 141. The value of M, as shown, for which the rod will be in equilibrium is 146. A wire of mass m is bent in the form of an arc of )&"'( %&"'( radius r subtending angle at the centre as shown. The moment of inertia of the wire about an axis passing through the centre and perpendicular to plane of wire is !"#$ ! (1) 1 kg (2) 2 kg (3) 4 kg (4) 6 kg θ 142. The minimum coefficient of friction for a solid sphere to roll without slipping on an inclined plane of inclination 45º is " ! (1) mr 2 (2) !" ! (1) (2) ! # " !! " !!" ! $ # (3) !" # ! $ (4) (3) (4) $ % " & " " 147. A solid sphere of mass m is rolling without 143. A wheel is rolling along a horizontal ground with a slipping on a horizontal floor such that velocity of speed of centre of mass is 10 m/s. The magnitude its centre of mass is v. Rotational kinetic energy of the velocity of the points at the extremities of associated with the body is the horizontal diameter of the wheel is equal to !" ! !" ! (1) (2) (1) ! $/ m/s (2) 20 m/s ! ! !" ! !" ! (3) !# m/s (4) $/ ! m/s (3) (4) " " Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ Last Leap for NEET (Part-I) System of Particles and Rotational Motion 17 148. Nm is the unit of % 154. A child of mass is standing at the centre of (1) Momentum ! a horizontal circular platform of mass M and radius (2) Angular momentum R rotating with angular speed about an axis (3) Coefficient of viscosity passing through the centre and perpendicular to the plane. The angular speed of the system when (4) Torque child shifts to the edge of the platform is 149. The formula for centripetal acceleration in circular motion is (symbols have their usual meaning) (1) ! ! ! ! ! (1) ! (2) ! (2) ! ! (3) ! ! (4) ! ! (3) 2 150. A particle moves in a circular path of radius R with a uniform angular speed rad/s. The acceleration (4) 3 of the particle after n revolutions is 155. Moment of inertia of a uniform circular disc about ! an axis through its edge and normal to the plane (1) (2) R 2 is I. Moment of inertia of the same disc about its ! diameter is ! (3) R (4) ! ! ! (1) (2) " % 151. A small object of uniform density rolls up a curved surface with an initial velocity v without slipping. It ! ! (3) (4) !" !" !! ! reaches up to a maximum height of with 156. Two solid spheres of masses M1 and M2 and radii "" respect to the initial position. The object is R1 and R2 respectively are released from the top of a rough inclined plane of height h. The spheres are (1) Ring rolling without slipping. If M1 : M2 = 4 and R1 : R2 = (2) Solid sphere 2 then ratio of the velocities of two spheres at the bottom of the plane is (3) Hollow sphere (1) 1 : 1 (2) 2 : 1 (4) Disc (3) 1 : 2 (4) 1 : 4 !!" !" 152. In horizontal circular motion, if and !! are 157. Angular momentum of particle remains conserved angular acceleration and centripetal acceleration when respectively, then correct option is (1) External net force on system is zero !" !!" !" !!" (2) Axis of rotation is moving with constant (1) ! !! ! " (2) !! ! velocity !" !!" !" !!" (3) Net torque is zero (3) !! ! !! ! (4) All of these (4) Both (1) & (2) 153. Which of the following regarding uniform horizontal 158. A uniform rod of mass m and length l lying on a circular motion is not correct? smooth table is pivoted about one end. An impulse (1) Angular velocity is perpendicular to the linear J is applied to the other end. Angular speed with velocity which rod starts rotating is (2) Angle between total acceleration and velocity "! $%& of particle is 90° (1) (2) "# $ (3) Acceleration of motion is not constant !! %%& (3) (4) (4) Acceleration of motion is constant "# $ Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 https://neetforsure.blogspot.com/ 18 System of Particles and Rotational Motion Last Leap for NEET (Part-I) 159. A solid sphere rolls down a rough inclined plane