## NEET AIPMT Physics Chapter Wise Solutions -System of Particles and Rotational Motion

NEET AIPMT Physics Chapter Wise SolutionsBiology Chemistry

**1. Point masses m _{1} and m_{2} are placed at the opposite ends of a rigid rod of 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 ω_{0} is minimum, is given by**

**2. An automobile moves on a road with a speed of 54 km h ^{-1}. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis j of rotation is 3 kg m^{2}. If the vehicle is brought to rest in 15 s, the magnitude of average torque j transmitted by its brakes to the wheel is i**

(a) 10.86 kg m2 s

^{-2}

(b) 2.86 kg m2 s

^{-2}

(c) 6.66 kg m2 s

^{-2}

(d) 8.58 kg m2 s

^{-2}

**(AIPMT 2015)**

**3. A force = a + 3 + 6 is acting at a point = 2 – 6 -2 . The value of a for which angular momentum about origin is conserved is**

(a) zero

(b) 1

(c) -1

(d) 2 **(AIPMT 2015)**

**4. 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 dfrom each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is**

**5. A mass m moves in a circle on a smooth horizontal plane with velocity v _{0} at a radius R_{0}. The mass is attached to a string which passes through a smooth hole in the plane as shown, The tension in the string is increased gradually and finally m moves in a circle of radius . The final value of the kinetic energy is**

**6. 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**

**7. A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound 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

(d) 157N** (AIPMT 2014)**

**8. The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle 0 without slipping and slipping down the incline without rolling is**

(a) 5:7

(b) 2:3

(c) 2:5

(d) 7:5 **(AIPMT 2014)**

**9. A rod PQ of mass M and length L is hinged at end P. The rod is p kept horizontal by a ™ massless stnng tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is**

**10. A small object of uniform density rolls up a curved surface with an initial velocity ‘V’. It reaches upto a maximum height of with respect to the initial position. The object is**

(a) hollow sphere

(b) disc

(c) ring

(d) solid sphere **(NEET 2013)**

**11. The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are**

**12. Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc Dt has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s ^{-1}. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocityof200 rad s^{-1}. The two discs are brought in contact face to &ce, with their axes of rotation coincident. The final angular velocity (in rad s^{-1}) of the system is**

(a) 60

(b) 100

(c) 120

(d) 40

**(Karnataka NEET 2013)**

**13. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along**

(a) a line perpendicular to the plane of rotation

(b) the line making an angle of 45° to the plane of rotation

(c) the radius

(d) the tangent to the orbit **(Prelims 2012)**

**14. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the center of mass of the system shifts by **

(a) 3.0 m

(b) 2.3 m

(c) zero

(d) 0.75 m **(Prelims 2012)**

**15. A car of mass 1000 kg negotiates a banked curve of radius 90 m on a ifictionless road. If the banking angle is 45°, the speed of the car is**

(a) 20ms^{-1}

(b) 30ms^{-1}

(c) 5ms^{-1}

(d) 10 ms^{-1} **(Prelims 2012)**

**16. ABC is an equilateral triangle with O as its centre. , and represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of **

**17. A car of mass m is moving on a level circular track of radius R. If μs represents the static friction between the road and types of the car, the maximum speed of the car in circular motion is given by**

**18. A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms ^{-1 }relative to the ground. Time taken by the man to complete one revolution is**

**19. The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through**

(a) B

(b) C

(c) D

(d) A **(Mains 2012)**

**20. Three masses are placed on the x-axis : 300 g at origin, 500 g at x=40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is**

(a) 40 cm

(b) 45 cm

(c) 50 cm

(d) 30 cm** (Mains 2012)**

**21. The instantaneous angular position of a point on a rotating wheel is given by the equation 0(0 = 2f ^{3} – 6t^{2} The torque on the wheel becomes zero at**

(a) t = 1 s

(b) t = 0.5 s

(c) t= 0.25 s

(d) t = 2 s

**(Prelims 2011)**

**22. The moment of inertia of a thin uniform rod of mass Mand length L about an axis passing through its midpoint and perpendicular to its length is I _{0}. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is**

**23. A small mass attached to a string rotates on a fiictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will**

(a) decrease by a factor of 2

(b) remain constant

(c) increase by a factor of 2

(d) increase by a factor of 4 **(Mains 2011)**

**24. A circular disk of moment of inertia I _{t }lt is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed of ω_{i}. Another disk of moment of inertia I_{b} is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ω_{f} Of The energy lost**

**25. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be**

(a) 2v

(b) zero

(c) 1.5v

(d) v (Prelims 2010)

**26. A gramophone record is revolving with an angular velocity a). A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ. The coin will revolve with the record if **

**27. From a circular disc of radius R and mass 9M, small disc of mass M and radius is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is**

**28. 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 only when angle of inclination of plane is 45°

(b) Both together

(c) Hollow cylinder

(d) Solid cylinder **(Mains 2010)**

**29. A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity to. 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**

**30. A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity to. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity vector r and x be the torque of this force about the origin, then**

**31.If is the force acting on a particle having position vector and be the torque of this force about the origin, then**

**32. Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is**

**33. Two bodies of mass 1 kg and 3 kg have position vectors + + and -3-2 + , respectively. The centre of mass of this system has a position vector**

**34. A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane define by the two halves of the rod is **

**35. 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**

**36. A particle of mass m y moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of- the particle with respect to origin O is L**_{A }**when it is at A and L _{B} when it is at B, then**

**37. A uniform rod 45 of length l,and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml ^{2}/3, the initial angular acceleration of the rod will be**

**38. A wheel has angular acceleration of 3.0 rad/sec ^{2} and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of**

(a) 10

b) 12

(c) 4

(d) 6. (2007)

**39. The moment of inertia of a uniform circular discof radius R and mass M about an axis touching the disc at its diameter and normal to the disc**

**40. The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is**

**41. A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force**

(a) dissipates energy as heat

(b) decreases the rotational motion

(c) decreases the rotational and translational motion

(d) converts translational energy to rotational energy.** (2005)**

**42. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio**

(a) 2 : 1

(b) 1 : 2

(c) : 1

(d) 1 : **(2005)**

**43. Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side / cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm ^{2} units will be**

**44. Consider a system of two particles having masses m _{1} and m_{2}. If the particle of mass m_{1} is pushed towards the mass centre of particles through a distance d, by what distance would be particle of mass m_{2} move so as to keep the mass centre of particles at the original position ?**

**45. A wheel having moment of inertia 2 kg-m ^{2} about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in one minute would be**

**46. A round disc of moment of inertia I _{2} about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I_{1}, rotating with an angular velocity to about the same axis. The final angular velocity of the combination of discs is**

**47. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is**

(a) 2 : 3

(b) 2 : 1

(c) :

(d) 1: ** (2004)**

**48. A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is**

**49. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be**

**50. 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 ?**

**51. A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity to. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be**

**52. A rod of length is 3 m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at**

(a) 1.5 m

(b) 2 m

(c) 2.5 m

(d) 3.0 m.** (2002)**

**53. A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (If radius of wheel is 1 m)**

**54. 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 centre of mass, which is correct?**

(a) h = R

(b) h = 2R

(c) h = 0 ,

(d) no relation between h and R. **(2002)**

**55. A disc is rotating with angular speed ω. If a child sits on it, what is conserved**

(a) linear momentum

(b) angular momentum

(c) kinetic energy

(d) potential energy. **(2002)**

**56. A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with**

(a) aluminium at interior and iron surround to it

(b) iron at interior and aluminium surround to it

(c) using iron and aluminium layers in alternate order

(d) sheet of iron is used at both external surface and aluminium sheet as internal layers. **(2002)**

**57. A disc is rolling, the velocity of its centre of mass is v _{cm}. Which one will be correct?**

(a) the velocity of highest point is 2 v

_{cm}and point of contact is zero

(b) the velocity of highest point is v

_{cm}and point of contact is v

_{cm}

(c) the velocity of highest point is 2v

_{cm}and point of contact is v

_{cm}

(d) the velocity of highest point is 2v

_{cm}and point of contact is 2v

_{cm}.

**(2001)**

**58. For the adjoining diagram, the correct relation between I _{1 },I_{2} and I**

_{3 }**is, (I – moment of inertia)**

**59. For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier**

(a) solid cylinder

(b) hollow cylinder

(c) both simultaneously

(d) can’t say anything.** (2000)**

**60. As shown in the figure atpoint O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break**

(a) A

(b) B

(c) C .

(d) D. **(2000)**

**61. Three identical metal balls, each of the radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at**

(a) line joining centres of any two balls

(b) centre of one of the balls

(c) horizontal surface

(d) point of intersection of the medians **(1999)**

**62. The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel to its diameter is**

**63. Find the torque of a force = – 3+ + 5 acting at the point r =l + 3 + **

**64. The centre of mass of system of particles does not depend on**

(a) position of the particles

(b) relative distances between the particles

(c) masses of the particles

(d) forces acting on the particle.** (1997)**

**65. A couple produces**

(a) linear and rotational motion

(b) no motion

(c) purely linear motion

(d) purely rotational motion. **(1997)**

**66. The ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I _{AB }, I_{BC } and I_{AC } are the moments of inertia of the plate about AB, BC and CA respectively. Which one of the following relations is correct?**

**67. What is the torque of the force= 2– 3 + 4 N acting at the point =3+2 + 3 m about origin?**

(a) -6+6-12

(b) – 17+6 + 13

(c) 6-6 + 12

(d) 17 -6-13 . **(1995)**

**68. A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is**

(a)1/2

(b)1/6

(c) 7/10

(d) 2/7 **(1994)**

**69. In a rectangle ABCD (BC = 2AB). AFnThe moment of inertia is minimum along axis through i**

**70. A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then**

(a) solid sphere reaches the bottom first

(b) solid sphere reaches the bottom last

(c) disc will reach the bottom first

(d) all reach the bottom at the same time **(1993)**

**71. The speed of a homogenous solid sphere after rolling down an inclined plane/of vertical heighth form test without sliding is**

**72. If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by**

(a) 7: 10

(b) 2:5

(c) 10:7

(d) 5:7 **(1991)**

**73. A particle of mass m = 5 is moving with a uniform speed v = 3 in the XOY plane along the line Y=X+ 4. The magnitude of the angular momentum of the particle about the origin is**

(a) 60 units

(b) 40>/2 units

(c) zero

(d) 7.5 units

**(1991)**

**74. A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is**

(a) 0.6 kgm2

(b) 0.15 kgm2

(c) 0.8 kgm2

(d) 0.75 kgm2 **(1990)**

**75. The moment of inertia of a body about a given axis is 1.2 kgm ^{2}. Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/sec^{2} must be applied about that axis for a duration of**

(a) 4 s

(b) 2 s

(c) 8 s

(d) 10 s

**(1990)**

**76. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be**

(a) 5I

(b) 3I

(c) 6I

(d) 4I **(1990)**

**77. A solid homogenous sphere of mass M and radius is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere**

(a) total kinetic energy is conserved

(b) the angular momentum of the sphere about the point of contact with the plane is conserved

(c) only the rotational kinetic energy about the centre of mass is conserved

(d) angular momentum about the centre of mass of conserved **(1988)**

**78. A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity to. Its kinetic energy is**

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