MCQ Physics Chapter 7: SYSTEMS OF PARTICLES AND ROTATIONAL MOTION, HS 1st Year

 

Chapter: Systems of Particles and Rotational Motion

1. What is the motion of a block sliding down an inclined plane without any sideways movement?

• A. Rotational motion
• B. Pure translational motion
• C. Rolling motion
• D. Oscillatory motion

Answer: B. Pure translational motion

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2. What is the term for the fixed point about which a rigid body rotates?

• A. Pivot point
• B. Centre of mass
• C. Axis of rotation
• D. Point of contact

Answer: C. Axis of rotation

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3. In a rigid body rotation about a fixed axis, what is true about the motion of every particle in the body?

• A. All particles move in straight lines.
• B. Every particle moves in a circle with the center on the axis.
• C. Particles move with varying velocities but in the same direction.
• D. Only particles near the axis move.

Answer: B. Every particle moves in a circle with the center on the axis.

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4. Where does the center of mass of a uniform thin rod lie?

• A. At one end of the rod
• B. At the midpoint of the rod
• C. Depends on its mass distribution
• D. At a point one-fourth its length from one end

Answer: B. At the midpoint of the rod

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5. What physical quantity is the rotational analogue of force in linear motion?

• A. Moment of inertia
• B. Angular momentum
• C. Torque
• D. Angular velocity

Answer: C. Torque

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6. What is the relationship between angular velocity ($\omega$) and linear velocity ($v$) of a particle in a rigid body rotation?

• A. $v = r \omega$
• B. $\omega = v/r$
• C. $v = \omega^2 r$
• D. $v = r^2 \omega$

Answer: A. $v = r \omega$

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7. Which condition is necessary for a rigid body to be in mechanical equilibrium?

• A. The sum of forces on the body must be nonzero.
• B. The sum of torques on the body must be nonzero.
• C. Both the sum of forces and the sum of torques must be zero.
• D. The body must not be subjected to any forces.

Answer: C. Both the sum of forces and the sum of torques must be zero.

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8. What is the vector expression for angular momentum ($L$) of a particle?

• A. $L = p \cdot r$
• B. $L = r \times p$
• C. $L = m \cdot v$
• D. $L = v \times r$

Answer: B. $L = r \times p$

Chapter: Systems of Particles and Rotational Motion

9. What is the center of mass for two particles with equal masses placed at equal distances along a line?

• A. At the midpoint between the particles
• B. Closer to the heavier particle
• C. At the position of one of the particles
• D. Outside the line joining the particles

Answer: A. At the midpoint between the particles

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10. For a system of particles, what is true about the motion of the center of mass under external forces?

• A. It is independent of external forces.
• B. It moves as if all the mass were concentrated at that point.
• C. It always remains stationary.
• D. It depends only on internal forces.

Answer: B. It moves as if all the mass were concentrated at that point.

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11. Which of the following conditions ensures translational equilibrium of a rigid body?

• A. The sum of all external forces is zero.
• B. The sum of all torques is zero.
• C. The angular velocity is constant.
• D. The center of mass is stationary.

Answer: A. The sum of all external forces is zero.

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12. Which of the following represents the scalar expression for torque ($\tau$)?

• A. $\tau = r \cdot F$
• B. $\tau = r F \sin\theta$
• C. $\tau = r \times F \cos\theta$
• D. $\tau = m r^2 \omega$

Answer: B. $\tau = r F \sin\theta$

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13. What is the SI unit of torque?

• A. Joule
• B. Newton-second
• C. Newton-meter
• D. Watt

Answer: C. Newton-meter

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14. What happens to the angular momentum of a system of particles if the net external torque is zero?

• A. It decreases.
• B. It remains constant.
• C. It increases.
• D. It becomes zero.

Answer: B. It remains constant.

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15. For a rigid body in rotational motion about a fixed axis, which of the following is true for the linear velocity ($v$) of a particle?

• A. $v$ is constant for all particles.
• B. $v$ is proportional to the perpendicular distance from the axis of rotation.
• C. $v$ is zero for all particles.
• D. $v$ is the same for particles at different radii.

Answer: B. $v$ is proportional to the perpendicular distance from the axis of rotation.

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16. The angular velocity ($\omega$) of a rigid body is a:

• A. Scalar quantity
• B. Vector quantity
• C. Dimensionless quantity
• D. Constant

Answer: B. Vector quantity

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17. The rolling motion of a cylinder down an inclined plane is a combination of:

• A. Pure translational motion and oscillation
• B. Pure rotation and vibration
• C. Pure translational motion and pure rotation
• D. Pure translational motion and precession

Answer: C. Pure translational motion and pure rotation

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18. Which physical quantity is the rotational analogue of mass in linear motion?

• A. Angular velocity
• B. Torque
• C. Moment of inertia
• D. Angular momentum

Answer: C. Moment of inertia

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19. Which force component contributes to torque about a given point?

• A. The parallel component of the force
• B. The perpendicular component of the force
• C. The total force
• D. None of the above

Answer: B. The perpendicular component of the force

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20. In rotational motion, which of the following is true for angular acceleration ($\alpha$)?

• A. $\alpha = \frac{d\omega}{dt}$
• B. $\alpha = \frac{dv}{dt}$
• C. $\alpha = \omega^2 r$
• D. $\alpha = \frac{d\tau}{dt}$

Answer: A. $\alpha = \frac{d\omega}{dt}$

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21. What happens to a particle on the axis of rotation in rigid body rotation about a fixed axis?

• A. It moves with the same velocity as other particles.
• B. It moves in a circle with a radius equal to its distance from the axis.
• C. It remains stationary.
• D. It moves in a straight line along the axis.

Answer: C. It remains stationary.

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22. What is the condition for a rigid body to have pure rotational motion?

• A. All parts of the body must have the same linear velocity.
• B. The body must rotate around a fixed axis.
• C. The center of mass must remain stationary.
• D. All external forces must cancel out.

Answer: B. The body must rotate around a fixed axis.

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23. The center of mass of a system of particles is:

• A. The point where all external forces act.
• B. A fixed point within the system.
• C. The average position of the system’s mass weighted by individual particle masses.
• D. Always at the geometric center of the system.

Answer: C. The average position of the system’s mass weighted by individual particle masses.

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24. In a rigid body, how do angular velocities of particles compare?

• A. All particles have different angular velocities.
• B. Angular velocity is constant for all particles.
• C. Angular velocity is zero for particles at the center of mass.
• D. Angular velocity varies with the radius of the circle described by the particles.

Answer: B. Angular velocity is constant for all particles.

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25. What is the dimensional formula for torque?

• A. $[ML^2T^{-2}]$
• B. $[MLT^{-2}]$
• C. $[ML^2T^{-3}]$
• D. $[MLT^{-1}]$

Answer: A. $[ML^2T^{-2}]$

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26. In an example of rotational motion, what happens to angular momentum if no external torque is applied?

• A. It increases linearly.
• B. It remains constant.
• C. It decreases exponentially.
• D. It oscillates with time.

Answer: B. It remains constant.

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27. For a system of particles, what does the total angular momentum ($L$) depend on?

• A. Linear velocities only
• B. Moment of inertia and angular velocity
• C. Total external torque only
• D. Gravitational forces only

Answer: B. Moment of inertia and angular velocity

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28. In pure translational motion of a rigid body, the orientation of the body:

• A. Remains constant.
• B. Changes continuously.
• C. Depends on the center of mass motion.
• D. Becomes independent of time.

Answer: A. Remains constant.

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29. When is the torque on a body maximum?

• A. When the force is parallel to the position vector.
• B. When the force is perpendicular to the position vector.
• C. When the force acts through the center of mass.
• D. When the position vector and force are in opposite directions.

Answer: B. When the force is perpendicular to the position vector.

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30. The conservation of angular momentum can be derived from:

• A. Newton’s first law
• B. Newton’s second law
• C. Newton’s third law
• D. The absence of external torque

Answer: D. The absence of external torque

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31. What is the motion of the center of mass in the absence of external forces?

• A. It accelerates continuously.
• B. It moves with constant velocity.
• C. It rotates about a fixed point.
• D. It oscillates along a straight line.

Answer: B. It moves with constant velocity.

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32. Which of the following conditions leads to equilibrium of a rigid body?

• A. The sum of external forces is zero and the sum of external torques is non-zero.
• B. The sum of external forces and torques are both zero.
• C. The net force on the center of mass is zero.
• D. The angular velocity is constant.

Answer: B. The sum of external forces and torques are both zero.

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33. Which of the following quantities is conserved in an isolated system with no external forces?

• A. Linear velocity
• B. Angular velocity
• C. Momentum
• D. Torque

Answer: C. Momentum

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34. In a rolling motion, what is the velocity of the point of contact with the surface if there is no slipping?

• A. Equal to the velocity of the center of mass
• B. Double the velocity of the center of mass
• C. Zero
• D. Depends on the radius

Answer: C. Zero

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     a) Newton
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     c) Joule
     d) Watt
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   • Example:
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     b) 11 m/s
     c) 10 m/s
     d) 20 m/s
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     b) Law of Inertia
     c) Law of Gravitation
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   • Example:
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     b) 9.8 m/s²
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