NEET Physics: System of Particles and Rotational Motion — Practice Set 3

Q1. Which of the following correctly describes the rotational kinetic energy of a rigid body?

A. \( K = \frac{1}{2} m v^2 \)
B. \( K = \frac{1}{2} I \omega^2 \)
C. \( K = I \omega \)
D. \( K = m \omega^2 \)

Q2. A wheel with moment of inertia \( 4 \, \text{kg m}^2 \) rotates at \( 3 \, \text{rad/s} \). A torque of \( 12 \, \text{Nm} \) acts for \( 2 \, \text{s} \). What is its final angular velocity?

A. 7 rad/s
B. 9 rad/s
C. 11 rad/s
D. 13 rad/s

Q3. A torque of \( 18 \, \text{Nm} \) acts on a wheel with moment of inertia \( 9 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 6 \, \text{s} \)?

A. 10 rad/s
B. 11 rad/s
C. 12 rad/s
D. 13 rad/s

Q4. Why can a rigid body fixed at one point only undergo rotational motion?

A. Because it has no mass
B. Because translational motion is impossible when fixed
C. Because it lacks angular velocity
D. Because it deforms under forces

Q5. A uniform disk of mass \( 2 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) rotates about its center. What is its moment of inertia?

A. 0.08 kg m²
B. 0.09 kg m²
C. 0.10 kg m²
D. 0.12 kg m²

Q6. In a rigid body, why does the point of application of force affect torque?

A. Because force magnitude changes
B. Because perpendicular distance from the axis changes
C. Because angular velocity changes
D. Because mass distribution changes

Q7. What is the physical significance of the moment of inertia in rotational motion?

A. It measures the speed of rotation
B. It measures resistance to angular acceleration
C. It measures the force applied
D. It measures the angular displacement

Q8. For a rigid body to be in rotational equilibrium, what condition must be satisfied?

A. The net force must be zero
B. The net torque must be zero
C. The angular velocity must be zero
D. The moment of inertia must be zero

Q9. Four particles of masses \( 1 \, \text{kg} \), \( 3 \, \text{kg} \), \( 5 \, \text{kg} \), and \( 7 \, \text{kg} \) are at \( (0, 0) \), \( (2, 0) \), \( (0, 3) \), and \( (2, 3) \) respectively. What is the y-coordinate of their center of mass?

A. 2.0 m
B. 2.25 m
C. 2.5 m
D. 2.75 m

Q10. A particle rotates about a fixed axis at a radius of \( 1.2 \, \text{m} \) with an angular velocity of \( 4 \, \text{rad/s} \). What is its linear speed?

A. 4.5 m/s
B. 4.8 m/s
C. 5.0 m/s
D. 5.2 m/s

Q11. A solid cylinder of mass \( 6 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) has an angular momentum of \( 10.8 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

A. 35 rad/s
B. 40 rad/s
C. 45 rad/s
D. 50 rad/s

Q12. Two vectors are \( \mathbf{a} = 5 \, \hat{\mathbf{i}} + 2 \, \hat{\mathbf{j}} \) and \( \mathbf{b} = -3 \, \hat{\mathbf{i}} + 4 \, \hat{\mathbf{j}} \). What is the magnitude of \( \mathbf{a} \times \mathbf{b} \)?

A. 24
B. 25
C. 26
D. 27

Q13. A hollow cylinder of mass \( 6 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) has an angular momentum of \( 10.8 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

A. 18 rad/s
B. 19 rad/s
C. 20 rad/s
D. 21 rad/s

Q14. What is the physical meaning of angular momentum in rotational motion?

A. The force causing rotation
B. The measure of rotational inertia and angular velocity
C. The resistance to linear motion
D. The acceleration of rotation

Q15. A solid cylinder of mass \( 3 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) rotates at \( 7 \, \text{rad/s} \). What is its angular momentum about its axis?

A. 2.5 kg m²/s
B. 2.625 kg m²/s
C. 2.8 kg m²/s
D. 3.0 kg m²/s

Physics — System of Particles and Rotational Motion

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Which of the following correctly describes the rotational kinetic energy of a rigid body?

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