NEET Physics: System of Particles and Rotational Motion — Practice Set 1

Q1. In pure rotational motion about a fixed axis, what is true about the motion of particles in a rigid body?

A. All particles move in straight lines
B. All particles move in circles with centers on the axis
C. Particles move randomly in all directions
D. Only particles on the axis move in circles

Q2. A hollow cylinder of mass \( 3 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) rotates about its axis with an angular speed of \( 6 \, \text{rad/s} \). What is its rotational kinetic energy?

A. 4.5 J
B. 4.9 J
C. 5.2 J
D. 5.5 J

Q3. A \( 3 \, \text{kg} \) block moves with a velocity of \( 5 \, \text{m/s} \) along the y-axis. What is the magnitude of the velocity of its center of mass?

A. 3 m/s
B. 4 m/s
C. 5 m/s
D. 6 m/s

Q4. What does torque represent in rotational motion?

A. The linear force applied to a body
B. The rotational effect of a force about an axis
C. The mass distribution of a body
D. The velocity of rotation

Q5. In rotational kinematics, what is the rotational analogue of linear acceleration?

A. Angular velocity
B. Angular acceleration
C. Torque
D. Moment of inertia

Q6. What is the unit of torque in the SI system?

A. kg m/s²
B. N m
C. kg m²/s²
D. rad/s²

Q7. Vectors \( \mathbf{a} = 2 \, \hat{\mathbf{i}} + 6 \, \hat{\mathbf{j}} \) and \( \mathbf{b} = 5 \, \hat{\mathbf{i}} - 3 \, \hat{\mathbf{j}} \) are given. What is the magnitude of \( \mathbf{a} \times \mathbf{b} \)?

A. 34
B. 35
C. 36
D. 37

Q8. A \( 5 \, \text{kg} \) object moves with a velocity of \( -3 \, \hat{\mathbf{i}} + 6 \, \hat{\mathbf{j}} \, \text{m/s} \). What is the magnitude of the velocity of its center of mass?

A. 6.5 m/s
B. 6.71 m/s
C. 6.9 m/s
D. 7.0 m/s

Q9. A thin ring of mass \( 3 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) has an angular momentum of \( 5.4 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

A. 15 rad/s
B. 18 rad/s
C. 20 rad/s
D. 22 rad/s

Q10. A \( 2 \, \text{kg} \) mass is attached to a \( 1 \, \text{m} \) long string and rotates in a horizontal circle. If its linear speed is \( 3 \, \text{m/s} \), what is its angular momentum about the center?

A. 4 kg m²/s
B. 5 kg m²/s
C. 6 kg m²/s
D. 7 kg m²/s

Q11. A thin ring of mass \( 4 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) rolls without slipping with a linear speed of \( 5 \, \text{m/s} \). What is its angular velocity?

A. 8 rad/s
B. 10 rad/s
C. 12 rad/s
D. 14 rad/s

Q12. A \( 5 \, \text{kg} \) mass rotates in a circle of radius \( 0.4 \, \text{m} \) with a speed of \( 3 \, \text{m/s} \). What is its angular momentum about the center?

A. 5.5 kg m²/s
B. 6.0 kg m²/s
C. 6.5 kg m²/s
D. 7.0 kg m²/s

Q13. Why is the vector product of two parallel vectors zero?

A. Because their magnitudes are zero
B. Because the angle between them is zero or 180°
C. Because they lie in different planes
D. Because their directions are opposite

Q14. What is the primary difference between translational and rotational motion of a rigid body?

A. Translational motion involves rotation about an axis
B. Rotational motion involves all particles moving with the same linear velocity
C. Translational motion involves all particles moving with the same velocity, while rotational motion involves the same angular velocity
D. Rotational motion occurs without an axis

Q15. A hollow cylinder of mass \( 3 \, \text{kg} \) and radius \( 0.8 \, \text{m} \) rolls without slipping with an angular velocity of \( 6 \, \text{rad/s} \). What is its linear speed?

A. 4.0 m/s
B. 4.5 m/s
C. 4.8 m/s
D. 5.0 m/s

Physics — System of Particles and Rotational Motion

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In pure rotational motion about a fixed axis, what is true about the motion of particles in a rigid body?

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