Rotational Motion Questions

-- 50. A bob of mass m attached to a string rotates in a horizontal circle (conical pendulum). About the point of suspension:

-- 49. Two discs (ω1=2, ω2=5) are brought into contact. Final ω = 4. If I2 = 1x10⁻³ kg m², then I1 is:

-- 48. The moment of inertia of a circular disc (M, R) is I0. Another disc of same mass and thickness but half the density has moment of inertia:

-- 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:

-- 46. Three identical spherical shells, each of mass m and radius r are placed in a row. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system is:

-- 45. 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:

-- 44. An automobile moves on a road with a speed of 54 km/h. The radius of its wheels is 0.45 m 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

-- 43. Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm. The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² units will be:

-- 42. If I_xy is the moment of inertia of a ring about a tangent in the plane of the ring and I_x'y' is the moment of inertia of a ring about a tangent perpendicular to the plane of the ring then:

-- 41. Of the two eggs which have identical sizes, shapes and weights, one is raw, and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is:

40. A force F = αî + ĵ + 3k̂ is acting at a point r = 2î - 6ĵ - 12k̂. The value of α for which angular momentum about origin is conserved is:

-- 39. Point masses 1, 2, 3 and 4 kg are lying at the points (0, 0, 0), (2, 0, 0), (0, 3, 0) and (–2, –2, 0) respectively. The moment of inertia of this system about X-axis will be

-- 38. For a given mass and size, moment of inertia of a solid disc is

-- 37. A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q. When string is cut, the initial angular acceleration of the rod is

-- 36. The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through (Assume points A, B, C, D where B is center and others are towards the edge)

-- 35. Carefully match column I and column II and choose the correct option.Column I: (A) Rolling motion, (B) Rate of change of angular momentum, (C) MI of hollow cylinder about axis, (D) Theorem of parallel axesColumn II: (1) Torque, (2) Rotatory mo

-- 34. Assertion A: An ice-skater stretches out arms-legs during performance.Reason R: Stretching out arms-legs helps the performer to balance his or her body so that he or she does not fall.

-- 33. If the angular momentum of a particle of mass m rotating along a circular path of radius r with uniform speed is L, the centripetal force acting on the particle is

-- 32. Assertion A: A particle is moving on a straight line with a uniform velocity, its angular momentum is always zero.Reason R: The linear momentum is not zero when particle moves with a uniform velocity.

31. Consider the following statements and select the correct statement(s).I. Two satellites of equal masses orbiting the earth at different heights have equal moments of inertia.II. If earth were to shrink suddenly, length of the day will increase.II

-- 17. 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

-- 16. The time rate of change of angular momentum of a particle is equal to

-- 15. During summersault, a swimmer bends his body to

-- 14. Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is

-- 13. According to the principle of conservation of angular momentum, if moment of inertia of a rotating body decreases, then its angular velocity

-- 12. Which of the following is invalid equation?(where τ, ω, L and α have their usual meanings)

-- 11. Which of the following statements about angular momentum is correct?

-- 10. In rotatory motion, linear velocities of all particles of the body are

-- 9. Rotational analogue of force in linear motion is

-- 8. Radius of gyration of body depends upon

-- 7. 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 le

-- 6. Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then

-- 5. The moment of inertia of a ...A... body about an axis ...B... to its plane is equal to the sum of its moments of inertia about two ...C... axes concurrent with perpendicular axis and lying in the plane of the body.Here, A, B and C refer to

-- 4. A boy comes and sits suddenly on a circular rotating table. What will remain conserved for the table-boy system?

-- 3. 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 angula

-- 2. The angular momentum of a system of particle is conserved

1. When sand is poured on a rotating disc, its angular velocity will

-- 6. A particles moving in a circular path has an angular momentum of L. If the frequency of rotation is halved, then its angular momentum becomes

-- 5. A circular disc A and a ring B have same mass and same radius. If they are rotated with the same angular speed about their own axis, then

-- 4. In rotation of a rigid body about a fixed axis, every....A....of the body moves in a ...B..., which lies in a plane ...C... to the axis and has its centre on the axis.Here, A, B and C refer to

-- 3. Assertion A: Moment of inertia of a particle is same, whatever be the axis of rotation.Reason R: Moment of inertia depends on mass and distance of the particles from the axis of rotation.

-- 2. If two circular discs A and B are of same mass but of radii r and 2r respectively, then the moment of inertia of A is

1. 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 momenta will be in the ratio

-- 4. 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 ω about the same axis. The final angular veloc

-- 3. One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moments of inertia about their diameters are respectively I_A and I_B, such that

-- 2. A planet is moving around the sun in an elliptical orbit. Its speed is

1. A wheel having moment of inertia 2 kg-m² 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

-- 6. After 2s stone is at 30° to horizontal, after 2s more it is horizontal. Initial velocity is:

-- 5. Magnitude of relative velocity of A w.r.t. B from x-t graph is:

-- 4. A wheel having moment of inertia 2 kg-m² 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