Phy-7: System of Particles and Rotational Motion30 Questions
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1. The point at which the entire mass of a body can be assumed to be concentrated for analysing translational motion is called the:
A. Centre of mass
B. Centre of gravity always
C. Centroid only
D. Point of equilibrium
Answer: A. Centre of mass
Explanation: The centre of mass is the unique point where the total mass of a system can be considered concentrated for the purpose of analysing its overall motion.
2. For a system of particles, the centre of mass moves as if:
A. All the mass were concentrated there and all external forces were applied there
B. It has no relation to external forces
C. Each particle moves independently
D. It always remains stationary
Answer: A. All the mass were concentrated there and all external forces were applied there
Explanation: The motion of the centre of mass follows Newton's laws as though the entire system's mass and all external forces act at that single point.
3. The turning effect of a force about an axis is called:
A. Torque
B. Momentum
C. Power
D. Work
Answer: A. Torque
Explanation: Torque measures the rotational effect produced by a force acting at some distance from an axis of rotation.
4. The formula for torque is given by:
A. τ = r × F (r cross F)
B. τ = r + F
C. τ = r/F
D. τ = rF only when parallel
Answer: A. τ = r × F (r cross F)
Explanation: Torque is calculated as the cross product of the position vector (r) and the applied force (F), incorporating the perpendicular distance and force magnitude.
5. The rotational analogue of linear momentum is called:
A. Angular momentum
B. Torque
C. Moment of inertia
D. Angular velocity
Answer: A. Angular momentum
Explanation: Angular momentum plays the same role in rotational motion as linear momentum does in translational motion.
6. The formula for angular momentum of a particle is given by:
A. L = r × p (r cross p)
B. L = rp only when parallel
C. L = r + p
D. L = r/p
Answer: A. L = r × p (r cross p)
Explanation: Angular momentum is defined as the cross product of the position vector (r) and linear momentum (p) of the particle.
7. The rotational analogue of mass, representing a body's resistance to change in rotational motion, is called:
A. Moment of inertia
B. Torque
C. Angular momentum
D. Angular velocity
Answer: A. Moment of inertia
Explanation: Moment of inertia quantifies how mass is distributed relative to the axis of rotation, analogous to how mass resists linear acceleration.
8. The moment of inertia of a body depends on its:
A. Mass distribution and distance from the axis of rotation
B. Colour and temperature
C. Only its total mass
D. Only its velocity
Answer: A. Mass distribution and distance from the axis of rotation
Explanation: Moment of inertia depends specifically on how the mass of an object is distributed relative to the chosen axis of rotation.
9. According to the principle of conservation of angular momentum, in the absence of external torque, the total angular momentum of a system remains:
A. Constant
B. Continuously increasing
C. Continuously decreasing
D. Always zero
Answer: A. Constant
Explanation: Just as linear momentum is conserved without external force, angular momentum remains constant when no net external torque acts on the system.
10. A rigid body is one in which the distances between all pairs of particles remain:
A. Constant, regardless of any external forces applied
B. Continuously changing
C. Zero at all times
D. Undefined
Answer: A. Constant, regardless of any external forces applied
Explanation: By definition, a rigid body does not deform, so the relative distances between its constituent particles remain fixed under external forces.
11. The condition for mechanical equilibrium of a rigid body requires that both the net force and net:
A. Torque acting on it are zero
B. Velocity are maximum
C. Mass is zero
D. Momentum is maximum
Answer: A. Torque acting on it are zero
Explanation: For complete equilibrium, a rigid body must have both zero net translational force and zero net rotational torque acting upon it.
12. The centre of gravity of a uniform, symmetric body coincides with its:
A. Geometric centre
B. Edge only
C. Highest point
D. Lowest point
Answer: A. Geometric centre
Explanation: For bodies with uniform density and symmetric shape, the centre of gravity coincides exactly with the geometric centre.
13. The theorem stating that the moment of inertia about an axis through the centre of mass is related to the moment of inertia about a parallel axis is called the:
A. Parallel axis theorem
B. Perpendicular axis theorem
C. Centre of mass theorem
D. Angular momentum theorem
Answer: A. Parallel axis theorem
Explanation: The parallel axis theorem relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the centre of mass.
14. The theorem applicable specifically to planar (flat, 2D) bodies, relating moments of inertia about perpendicular axes, is the:
A. Perpendicular axis theorem
B. Parallel axis theorem
C. Torque theorem
D. Rigid body theorem
Answer: A. Perpendicular axis theorem
Explanation: The perpendicular axis theorem applies to flat, planar bodies, relating the moment of inertia about an axis perpendicular to the plane to the two in-plane axes.
15. Angular velocity is defined as the rate of change of:
A. Angular displacement with respect to time
B. Linear displacement with respect to time
C. Torque with respect to time
D. Mass with respect to time
Answer: A. Angular displacement with respect to time
Explanation: Angular velocity measures how quickly the angular position (angular displacement) of a rotating object changes over time.
16. For a rigid body rotating with constant angular velocity, the angular acceleration is:
A. Zero
B. Maximum
C. Continuously increasing
D. Undefined
Answer: A. Zero
Explanation: Since angular acceleration measures the rate of change of angular velocity, a constant angular velocity implies zero angular acceleration.
17. In rolling motion without slipping, a body's motion consists of:
A. Both translational and rotational motion combined
B. Only translational motion
C. Only rotational motion
D. No motion at all
Answer: A. Both translational and rotational motion combined
Explanation: Rolling without slipping involves a combination of the body's centre of mass moving forward (translation) while the body simultaneously spins (rotation).
18. The point of a rigid body that momentarily has zero velocity during pure rolling motion is the:
A. Point of contact with the surface
B. Centre of mass
C. Topmost point
D. Farthest point from the surface
Answer: A. Point of contact with the surface
Explanation: During pure rolling without slipping, the specific point of the rolling body touching the surface has zero instantaneous velocity.
19. A couple consists of two equal and opposite forces that are:
A. Not collinear, producing a net torque with zero net force
B. Collinear, producing zero net torque
C. Acting on the same point
D. Always parallel to displacement
Answer: A. Not collinear, producing a net torque with zero net force
Explanation: A couple involves two equal, opposite, non-collinear forces that create a rotational effect (torque) without any net translational force.
20. The SI unit of torque is the:
A. Newton-metre
B. Joule
C. Watt
D. Newton only
Answer: A. Newton-metre
Explanation: Torque, being a product of force and perpendicular distance, is measured in newton-metres (N·m).
21. The SI unit of angular momentum is:
A. kg m²/s
B. kg m/s
C. N m
D. kg m²
Answer: A. kg m²/s
Explanation: Angular momentum, derived from mass, velocity and distance, has SI units of kilogram metre squared per second.
22. A figure skater spinning faster after pulling their arms inward demonstrates:
A. Conservation of angular momentum
B. Conservation of linear momentum only
C. Newton's Third Law only
D. Loss of energy without conservation
Answer: A. Conservation of angular momentum
Explanation: By reducing their moment of inertia (pulling arms in), the skater's angular velocity increases to keep angular momentum constant.
23. The centre of mass of a system of particles is calculated using a weighted average based on each particle's:
A. Mass and position
B. Colour and shape
C. Velocity only
D. Temperature only
Answer: A. Mass and position
Explanation: The centre of mass position is found by taking the weighted average of individual particle positions, weighted according to their respective masses.
24. For two point masses connected by a rigid rod, the moment of inertia about an axis is calculated using the formula:
A. I = mr² summed for each mass
B. I = mr summed for each mass
C. I = m + r summed for each mass
D. I = m/r summed for each mass
Answer: A. I = mr² summed for each mass
Explanation: Moment of inertia for point masses is calculated by summing the product of each mass and the square of its distance from the axis.
25. The condition for translational equilibrium of a rigid body is that the vector sum of all external forces equals:
A. Zero
B. Maximum
C. The total mass
D. The total torque
Answer: A. Zero
Explanation: Translational equilibrium specifically requires that the net external force acting on the body sums to zero.
26. The condition for rotational equilibrium of a rigid body is that the vector sum of all external torques equals:
A. Zero
B. Maximum
C. The total force
D. The total mass
Answer: A. Zero
Explanation: Rotational equilibrium requires that the net external torque acting about any axis on the body is exactly zero.
27. In the absence of external torque, a spinning object with increasing moment of inertia will experience:
A. A decrease in angular velocity
B. An increase in angular velocity
C. No change in angular momentum's relation to velocity
D. An increase in mass
Answer: A. A decrease in angular velocity
Explanation: Since angular momentum (L = Iω) remains conserved, increasing the moment of inertia (I) causes angular velocity (ω) to decrease correspondingly.
28. The kinetic energy of a rotating rigid body is given by the formula:
A. 1/2 Iω²
B. 1/2 mv²
C. Iω
D. mIω
Answer: A. 1/2 Iω²
Explanation: Rotational kinetic energy is calculated using one-half the moment of inertia multiplied by the square of the angular velocity, analogous to linear kinetic energy.
29. The distribution of mass farther from the axis of rotation results in a moment of inertia that is:
A. Larger
B. Smaller
C. Unaffected
D. Zero
Answer: A. Larger
Explanation: Since moment of inertia depends on mass distribution relative to the axis (mr²), mass positioned farther away contributes a larger moment of inertia.
30. A wheel rolling without slipping down an incline gains both translational and rotational kinetic energy, which together account for its total:
A. Kinetic energy
B. Potential energy only
C. Torque only
D. Angular momentum only
Answer: A. Kinetic energy
Explanation: The total kinetic energy of the rolling wheel is the sum of its translational kinetic energy (motion of centre of mass) and rotational kinetic energy (spinning).
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