# Practice Test: Question Set - 03

**1. A disk with a rotational inertia of 5.0 kgm**

^{2}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)

*MR*

^{2}/2

- (B)

*ML*

^{2}/2

- (C)

*ML*

^{2}

- (D)

*MR*

^{2}

**3. The rotational inertia of a solid uniform sphere about a diameter is (2/5)**

*MR*^{2}, 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)

*MR*

^{2}

- (B) (2/5)

*MR*

^{2}

- (C) (3/5)

*MR*

^{2}

- (D) (7/5)

*MR*

^{2}

**4. A disk with a rotational inertia of 5.0 kg .m**

^{2}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/s

^{2}

- (C) 0.4 rad/s

^{2}

- (D) 1.0 rad/s

^{2}

**5. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10**

^{-3}kgm^{2}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/sec

^{2}

- (B) 0.020 m/sec

^{2}

- (C) 0.10 m/sec

^{2}

- (D) 0.20 m/sec

^{2}

**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/s**

^{2}of the wheel during this process is:- (A) 1/

*π*

- (B) 2

- (C) 4

- (D) 4

*π*

**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)

*ML*

^{2}/2

- (B)

*ML*

^{2}

- (C) 3

*ML*

^{2}/2

- (D) 5

*ML*

^{2}/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.m**

^{2}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**

*R*_{1}is mounted coaxially with a larger disk of radius*R*_{2}. 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)

*R*

_{1}

*F*/

*mR*

_{2}

- (B)

*R*

_{1}

*R*

_{2}

*F*/(

*I*–

*mR*

_{2}

^{2})

- (C)

*R*

_{1}

*R*

_{2}

*F*/(

*I*+

*mR*

_{2}

^{2})

- (D)

*R*

_{1}

*R*

_{2}

*F*/(

*I*–

*mR*

_{1}

*R*

_{2})

**13. A disk has a rotational inertia of 6.0 kgm**

^{2}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) 2

*π*

**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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