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Set 2 of 14 · Questions 31-60 of 410

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JEE Main Physics · Rotational Mechanics · Set 2 (Q31-60)

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  1. 31.
    Two rotating bodies A and B of masses m and 2m with moments of inertia and ( > ) have equal kinetic energy of rotation. If and be their angular momenta respectively, then
    1. (1) >
    2. (2)
    3. (3) =
    4. (4) >
  2. 32.
    The moment of inertia of a body about a given axis is 1.2 . Initially, the body is at rest. Inorder to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/ must be applied about that axis for a duration of
    1. (1)4
    2. (2)2
    3. (3)8
    4. (4)10
  3. 33.
    Consider a uniform wire of mass and length . It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  4. 34.
    From a circular disc of radius and mass , a small disc of mass 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
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  5. 35.
    A body rotating with uniform acceleration about its geometrical axis makes 8 rotations in the first 2 seconds. The number of rotations the body makes in the next 3 seconds is(Initially the body is at rest)
    1. (1)50
    2. (2)25
    3. (3)42
    4. (4)21
  6. 36.
    The ratio of the radii of two solid spheres of same mass is . The ratio of the moments of inertia of the spheres about their diameters is
    1. (1)4:9
    2. (2)
    3. (3)
    4. (4)
  7. 37.
    The magnitude of torque on a particle of mass is about the origin. If the force acting on it is and the distance of the particle from the origin is , the angle between the force and the position vector is (in radians):
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  8. 38.
    The ratio of radius of gyration of a solid sphere of mass and radius about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is [NEET 2023]
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  9. 39.
    A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm . The moment of inertia of this pair of spheres about the tangent passing through the point of contact is .
    1. (1)0.72
    2. (2)0.36
    3. (3)0.18
    4. (4)0.63
  10. 40.
    If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  11. 41.
    The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'Ι(x)'. Which one of the graphs represents the variation of Ι(x) with x correctly ?
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  12. 42.
    Consider a wheel rotating around a fixed axis. If the rotation angle varies with time as , then the total acceleration of a point on the rim of the wheel is ( being the tangential velocity)
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  13. 43.
    Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is . If the same rod is bent into a ring and its moment of inertia about its diameter is , then the ratio is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  14. 44.
    A disc of moment of inertia is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed . Another disc of moment of inertia having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed . The energy lost by the initial rotating disc is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  15. 45.
    The ratio of the accelerations for a solid sphere (mass and radius ) rolling down an incline of angle 6 without slipping and slipping down the incline without rolling is
    1. (1)5 : 7
    2. (2)2 : 3
    3. (3)2 : 5
    4. (4)7 : 5
  16. 46.
    The moment of the force, at , about the point , is given by [NEET 2018]
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  17. 47.
    A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy as well as rotational kinetic energy simultaneously. The ratio for the sphere is
    1. (1)7: 10
    2. (2)5: 7
    3. (3)10: 7
    4. (4)2: 5
  18. 48.
    The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of from it, is ' '. Which one of the graphs represents the variation of with correctly?
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  19. 49.
    The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is:
    1. (1)
    2. (2)
    3. (3)1
    4. (4)3
  20. 50.
    A solid sphere rolls without slipping on an inclined plane at an angle . The ratio of total kinetic energ? to its rotational kinetic energy is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  21. 51.
    A spherical bob of mass is attached to the end of a string having length . The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is . The maximum possible value of angular velocity of bob (in ) is
    1. (1)18
    2. (2)24
    3. (3)28
    4. (4)32
  22. 52.
    A force is acting at a point . The value of for which angular momentum about origin is conserved is
    1. (1)zero
    2. (2)1
    3. (3)
    4. (4)2
  23. 53.
    A wheel of moment of inertia is rotating about an axis passing through centre and perpendicular to its plane at a speed . Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  24. 54.
    A solid sphere of mass and radius 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. The ratio of their kinetic energies of rotation will be
    1. (1)2 : 3
    2. (2)1 : 5
    3. (3)1 : 4
    4. (4)3 : 1
  25. 55.
    The moment of inertia of a rectangular plate of mass , length and breadth , about an axis passing through its centre and perpendicular to its plane is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  26. 56.
    A body having a moment of inertia about its axis of rotation equal to is rotating with angular velocity of . Kinetic energy of this rotating body is same as that of a body of mass moving with velocity . The value of is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  27. 57.
    A thin circular ring of mass and radius is rotating about its axis with an angular speed . Two particleshaving mass each are now attached at diametrically opposite points. The angular speed of the ring will become:
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  28. 58.
    A uniform solid cylinder of length and radius has moment of inertia about its axis equal to . A small cocentric cylinder of length and radius carved from this cylinder has moment of inertia about its axis equals to . The ratio is .
  29. 59.
    A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is . The value of is_____
  30. 60.
    If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be______hours 30 minutes.