Rotational Inertia Mechanical Questions - Set 03 - ObjectiveBooks

Rotational Inertia Mechanical Questions - Set 03

Practice Test: Question Set - 03


1. A disk with a rotational inertia of 5.0 kgm2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:
    (A) 1.6 J
    (B) 2.5 J
    (C) 6.3 J
    (D) 10 J

2. The rotational inertia of a thin cylindrical shell of mass ‘M’, radius ‘R’, and length ‘L’ about its central axis (X - X') is
    (A) MR2/2
    (B) ML2/2
    (C) ML2
    (D) MR2

3. The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:
    (A) MR2
    (B) (2/5) MR2
    (C) (3/5) MR2
    (D) (7/5) MR2

4. A disk with a rotational inertia of 5.0 kg .m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied parallel to the axis. The angular acceleration of the disk is:
    (A) 0
    (B) 0.40 rad/s2
    (C) 0.4 rad/s2
    (D) 1.0 rad/s2

5. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10-3 kgm2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is:
    (A) 2.0 J
    (B) 4.0 J
    (C) 14 J
    (D) 22 J

6. String is wrapped around the periphery of a 5.0 cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:
    (A) 0.010 m/sec2
    (B) 0.020 m/sec2
    (C) 0.10 m/sec2
    (D) 0.20 m/sec2

7. If a wheel is turning at 3.0 rad/sec, the time it takes to complete one revolution is about:
    (A) 0.33 sec
    (B) 0.67 sec
    (C) 1.0 sec
    (D) 2.1 sec

8. A flywheel rotating at 12 rev/s is brought to rest in 6 sec. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:
    (A) 1/π
    (B) 2
    (C) 4
    (D) 4π

9. Three identical objects, each of mass ‘M’, are fastened to a mass less rod of length ‘L’ as shown. The rotational inertia about one end of the rod of this array is:
    (A) ML2/2
    (B) ML2
    (C) 3ML2/2
    (D) 5ML2/4

10. To increase the rotational inertia of a solid disk about its axis without changing its mass:
    (A) Drill holes near the rim and put the material near the axis
    (B) Drill holes near the axis and put the material near the rim
    (C) Drill holes at points on a circle near the rim and put the material at points between the holes
    (D) Drill holes at points on a circle near the axis and put the material at points between the holes

11. A disk with a rotational inertia of 5.0 kg.m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:
    (A) 0.57 rad/s
    (B) 0.64 rad/s
    (C) 0.80 rad/s
    (D) 1.6 rad/s

12. A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force F as shown. The acceleration of the block is:
    (A) R1F/mR2
    (B) R1R2F/(ImR22 )
    (C) R1R2F/(I + mR22 )
    (D) R1R2F/(ImR1R2)

13. A disk has a rotational inertia of 6.0 kgm2 and a constant angular acceleration of 2.0 rad/s². If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:
    (A) 0
    (B) 30 J 
    (C) 60 J 
    (D) 300 J 

14. The angular speed in rad/sec of the second hand of a watch is:
    (A) π/1800
    (B) π/60
    (C) π/30
    (D) 2π

15. A wheel starts from rest and has an angular acceleration of 4.0 rad/s². When it has made 10 rev its angular velocity is:
    (A) 16 rad/sec
    (B) 22 rad/sec
    (C) 32 rad/sec
    (D) 250 rad/sec

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