Chapter 6: Systems of Particles and Rotational Motion Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 1

Logic Check

Assertion (A): In pure translational motion, all particles of a rigid body have the same velocity at any instant. Reason (R): In pure translation, the angular velocity of the rigid body is zero.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 2

Logic Check

Assertion (A): The centre of mass of a uniform sphere lies at its geometric centre. Reason (R): For any body with a point of reflection symmetry, the centre of mass coincides with that point of symmetry.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 3

Logic Check

Assertion (A): The centre of mass of a system of particles always lies inside the body. Reason (R): The centre of mass is the point at which the entire mass of the system is assumed to be concentrated.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 4

Logic Check

Assertion (A): When a projectile explodes in mid-air, the centre of mass of its fragments continues along the same parabolic path. Reason (R): The explosion forces are internal to the system and do not affect the motion of the centre of mass; only the external gravitational force governs its trajectory.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 5

Logic Check

Assertion (A): The vector product a × b is equal to b × a. Reason (R): The vector product is commutative just like the scalar product.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 6

Logic Check

Assertion (A): The linear velocity of a particle at a greater perpendicular distance from the axis of rotation is larger than that of a particle closer to the axis, when both rotate with the same angular velocity. Reason (R): The relation v = ωr shows that linear velocity is directly proportional to the perpendicular distance r from the axis for a given ω.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 7

Logic Check

Assertion (A): Torque and work have the same dimensional formula. Reason (R): Torque and work are the same physical quantity.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 8

Logic Check

Assertion (A): For a rigid body in mechanical equilibrium, the choice of origin for calculating torques does not affect the rotational equilibrium condition. Reason (R): If translational equilibrium (net force = 0) holds, the net torque about any point is the same and equals zero regardless of the reference point.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 9

Logic Check

Assertion (A): A couple produces rotation without translation. Reason (R): The net force of a couple is zero, so there is no translational acceleration, but the net torque is non-zero, producing angular acceleration.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 10

Logic Check

Assertion (A): The centre of gravity and centre of mass of a body always coincide. Reason (R): Both the centre of gravity and centre of mass are defined using the distribution of mass in the body.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 11

Logic Check

Assertion (A): Moment of inertia of a body depends on the axis of rotation. Reason (R): Moment of inertia is defined as I = Σmᵢrᵢ², where rᵢ is the perpendicular distance of particle i from the chosen axis, which changes when the axis changes.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 12

Logic Check

Assertion (A): A hollow cylinder has a greater moment of inertia than a solid cylinder of the same mass and radius about their common axis. Reason (R): In the hollow cylinder, all mass is concentrated at the maximum distance R from the axis, whereas in the solid cylinder mass is distributed from 0 to R, resulting in a smaller average r².

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 13

Logic Check

Assertion (A): The kinematic equations for uniform angular acceleration are ω = ω₀ + αt, θ = θ₀ + ω₀t + ½αt², and ω² = ω₀² + 2α(θ−θ₀). Reason (R): These equations are derived by direct analogy, replacing x with θ, v with ω, and a with α in the linear kinematic equations.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 14

Logic Check

Assertion (A): For the same applied torque, a solid sphere acquires a greater angular acceleration than a hollow sphere of the same mass and radius about a diameter. Reason (R): The solid sphere has a smaller moment of inertia (2MR²/5) than the hollow sphere (2MR²/3) about a diameter, and since τ = Iα, smaller I gives larger α for the same τ.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 15

Logic Check

Assertion (A): When a diver tucks the body during a dive, the angular speed increases. Reason (R): Tucking reduces the moment of inertia; by conservation of angular momentum (Iω = constant), angular speed must increase.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 16

Logic Check

Assertion (A): The work done by a torque τ in producing an angular displacement θ is W = τθ. Reason (R): Work done in rotational motion is entirely analogous to work done in translational motion, with force replaced by torque and displacement replaced by angular displacement.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 17

Logic Check

Assertion (A): Angular momentum of a particle moving with constant velocity in a straight line is zero about all points. Reason (R): The perpendicular distance from any point to the line of motion is constant and non-zero unless the point lies on the line; hence angular momentum is non-zero and constant.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 18

Logic Check

Assertion (A): The total angular momentum of a system of particles is conserved when the total external torque is zero. Reason (R): By Newton's third law, internal torques between particles occur in equal and opposite pairs and sum to zero, so only external torques change the total angular momentum.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 19

Logic Check

Assertion (A): The radius of gyration of a body is a fixed intrinsic property independent of the axis of rotation. Reason (R): Radius of gyration k is defined by I = Mk²; since I depends on the axis, k also depends on the axis.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 20

Logic Check

Assertion (A): A flywheel with a large moment of inertia ensures smooth rotation of an engine. Reason (R): A large moment of inertia means the flywheel resists sudden changes in angular velocity, absorbing energy during high-torque strokes and releasing it during low-torque strokes.

Reasoning Options

ByteNotes

Chapter sections

Chapter 6: Systems of Particles and Rotational Motion | Assertion-Reason

Assertion (A): In pure translational motion, all particles of a rigid body have the same velocity at any instant. Reason (R): In pure translation, the angular velocity of the rigid body is zero.

Assertion (A): The centre of mass of a uniform sphere lies at its geometric centre. Reason (R): For any body with a point of reflection symmetry, the centre of mass coincides with that point of symmetry.

Assertion (A): The centre of mass of a system of particles always lies inside the body. Reason (R): The centre of mass is the point at which the entire mass of the system is assumed to be concentrated.

Assertion (A): The vector product a × b is equal to b × a. Reason (R): The vector product is commutative just like the scalar product.

Assertion (A): Torque and work have the same dimensional formula. Reason (R): Torque and work are the same physical quantity.

Assertion (A): A couple produces rotation without translation. Reason (R): The net force of a couple is zero, so there is no translational acceleration, but the net torque is non-zero, producing angular acceleration.

Assertion (A): The centre of gravity and centre of mass of a body always coincide. Reason (R): Both the centre of gravity and centre of mass are defined using the distribution of mass in the body.

Assertion (A): Moment of inertia of a body depends on the axis of rotation. Reason (R): Moment of inertia is defined as I = Σmᵢrᵢ², where rᵢ is the perpendicular distance of particle i from the chosen axis, which changes when the axis changes.

Assertion (A): When a diver tucks the body during a dive, the angular speed increases. Reason (R): Tucking reduces the moment of inertia; by conservation of angular momentum (Iω = constant), angular speed must increase.

Assertion (A): The work done by a torque τ in producing an angular displacement θ is W = τθ. Reason (R): Work done in rotational motion is entirely analogous to work done in translational motion, with force replaced by torque and displacement replaced by angular displacement.

Assertion (A): The total angular momentum of a system of particles is conserved when the total external torque is zero. Reason (R): By Newton's third law, internal torques between particles occur in equal and opposite pairs and sum to zero, so only external torques change the total angular momentum.

Assertion (A): The radius of gyration of a body is a fixed intrinsic property independent of the axis of rotation. Reason (R): Radius of gyration k is defined by I = Mk²; since I depends on the axis, k also depends on the axis.

Assertion (A): A flywheel with a large moment of inertia ensures smooth rotation of an engine. Reason (R): A large moment of inertia means the flywheel resists sudden changes in angular velocity, absorbing energy during high-torque strokes and releasing it during low-torque strokes.

Unlock all Assertion-Reason Questions

Practice in Quiz Mode