Chapter 13: Oscillations Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 1

Logic Check

Assertion (A): Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Reason (R): Circular motion is periodic but the body does not move to and fro about a mean position.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 2

Logic Check

Assertion (A): The time period of a simple pendulum depends on the mass of the bob. Reason (R): The restoring torque for a simple pendulum is τ = −mgL sin θ, which contains mass m.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 3

Logic Check

Assertion (A): The total mechanical energy of a particle executing SHM is constant. Reason (R): The spring force F = −kx is a conservative force, so mechanical energy is conserved.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 4

Logic Check

Assertion (A): In SHM, the acceleration is maximum at the mean position. Reason (R): Acceleration in SHM is given by a = −ω²x, so it is proportional to displacement.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 5

Logic Check

Assertion (A): The period of SHM does not depend on amplitude. Reason (R): The time period T = 2π/ω depends only on angular frequency ω, which is determined by k and m, not by amplitude A.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 6

Logic Check

Assertion (A): The velocity of a particle in SHM is zero at both extreme positions. Reason (R): At the extreme positions, all the mechanical energy is in the form of potential energy and kinetic energy is zero.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 7

Logic Check

Assertion (A): SHM can be viewed as the projection of uniform circular motion on a diameter of the reference circle. Reason (R): The force acting on a particle in linear SHM is the same as the centripetal force in the reference circle.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 8

Logic Check

Assertion (A): The kinetic and potential energies in SHM each have a period of T/2. Reason (R): Both kinetic energy (∝ sin²(ωt + φ)) and potential energy (∝ cos²(ωt + φ)) involve squared trigonometric functions, which repeat with period π.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 9

Logic Check

Assertion (A): For a simple pendulum, the motion is simple harmonic only for small angular displacements. Reason (R): For small angles θ (in radians), sin θ ≈ θ, making the restoring torque linearly proportional to θ.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 10

Logic Check

Assertion (A): The function e^(−ωt) represents a damped oscillation. Reason (R): The function e^(−ωt) decreases monotonically with time and never repeats its value, so it is non-periodic.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 11

Logic Check

Assertion (A): The restoring force in SHM is always directed toward the mean position. Reason (R): The force law for SHM is F = −kx, where the negative sign ensures force opposes displacement.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 12

Logic Check

Assertion (A): Two SHMs with the same amplitude and angular frequency but different phase constants have different total energies. Reason (R): Total energy of SHM is E = ½kA², which depends only on amplitude A and force constant k.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 13

Logic Check

Assertion (A): The combination of sin ωt + cos ωt represents simple harmonic motion. Reason (R): A linear combination of sine and cosine functions of the same angular frequency can always be written as a single sinusoidal function.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 14

Logic Check

Assertion (A): Attaching two identical springs (each of constant k) on both sides of a block results in a shorter time period compared to a single spring of constant k. Reason (R): The effective spring constant with two springs is 2k, and larger spring constant gives shorter period.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 15

Logic Check

Assertion (A): Displacement in oscillatory motion can represent quantities other than linear position, such as voltage or pressure. Reason (R): The chapter defines displacement as the change with time of any physical property under consideration.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 16

Logic Check

Assertion (A): The period of a simple pendulum increases when it is taken from Earth to the Moon. Reason (R): The time period T = 2π√(L/g) is inversely proportional to √g; the Moon's lower gravity increases T.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 17

Logic Check

Assertion (A): In SHM, when displacement is positive, acceleration is negative. Reason (R): Acceleration a = −ω²x; when x > 0, a < 0, confirming the restoring nature of the force.

Reasoning Options

ByteNotes

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 18

Logic Check

Assertion (A): The frequency of SHM of a spring-mass system increases if the spring constant is increased. Reason (R): Angular frequency ω = √(k/m); greater k gives greater ω and hence greater frequency ν = ω/2π.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 19

Logic Check

Assertion (A): The function sin² ωt represents simple harmonic motion about equilibrium at x = 0. Reason (R): sin² ωt = ½ − ½ cos 2ωt, which is a periodic function with equilibrium at x = ½, not at x = 0.

Reasoning Options

ByteNotes

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 20

Logic Check

Assertion (A): The projection of a particle undergoing uniform circular motion on the y-axis also executes SHM. Reason (R): The y-projection is y = A sin(ωt + φ), which is a sinusoidal function of time with the same amplitude and angular frequency as the x-projection.

Reasoning Options

ByteNotes

Chapter sections

Chapter 13: Oscillations | Assertion-Reason

Assertion (A): Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Reason (R): Circular motion is periodic but the body does not move to and fro about a mean position.

Assertion (A): The time period of a simple pendulum depends on the mass of the bob. Reason (R): The restoring torque for a simple pendulum is τ = −mgL sin θ, which contains mass m.

Assertion (A): The total mechanical energy of a particle executing SHM is constant. Reason (R): The spring force F = −kx is a conservative force, so mechanical energy is conserved.

Assertion (A): In SHM, the acceleration is maximum at the mean position. Reason (R): Acceleration in SHM is given by a = −ω²x, so it is proportional to displacement.

Assertion (A): The period of SHM does not depend on amplitude. Reason (R): The time period T = 2π/ω depends only on angular frequency ω, which is determined by k and m, not by amplitude A.

Assertion (A): The velocity of a particle in SHM is zero at both extreme positions. Reason (R): At the extreme positions, all the mechanical energy is in the form of potential energy and kinetic energy is zero.

Assertion (A): SHM can be viewed as the projection of uniform circular motion on a diameter of the reference circle. Reason (R): The force acting on a particle in linear SHM is the same as the centripetal force in the reference circle.

Assertion (A): The kinetic and potential energies in SHM each have a period of T/2. Reason (R): Both kinetic energy (∝ sin²(ωt + φ)) and potential energy (∝ cos²(ωt + φ)) involve squared trigonometric functions, which repeat with period π.

Assertion (A): For a simple pendulum, the motion is simple harmonic only for small angular displacements. Reason (R): For small angles θ (in radians), sin θ ≈ θ, making the restoring torque linearly proportional to θ.

Assertion (A): The function e^(−ωt) represents a damped oscillation. Reason (R): The function e^(−ωt) decreases monotonically with time and never repeats its value, so it is non-periodic.

Assertion (A): The restoring force in SHM is always directed toward the mean position. Reason (R): The force law for SHM is F = −kx, where the negative sign ensures force opposes displacement.

Assertion (A): Two SHMs with the same amplitude and angular frequency but different phase constants have different total energies. Reason (R): Total energy of SHM is E = ½kA², which depends only on amplitude A and force constant k.

Assertion (A): The combination of sin ωt + cos ωt represents simple harmonic motion. Reason (R): A linear combination of sine and cosine functions of the same angular frequency can always be written as a single sinusoidal function.

Assertion (A): Attaching two identical springs (each of constant k) on both sides of a block results in a shorter time period compared to a single spring of constant k. Reason (R): The effective spring constant with two springs is 2k, and larger spring constant gives shorter period.

Assertion (A): Displacement in oscillatory motion can represent quantities other than linear position, such as voltage or pressure. Reason (R): The chapter defines displacement as the change with time of any physical property under consideration.

Assertion (A): The period of a simple pendulum increases when it is taken from Earth to the Moon. Reason (R): The time period T = 2π√(L/g) is inversely proportional to √g; the Moon's lower gravity increases T.

Assertion (A): In SHM, when displacement is positive, acceleration is negative. Reason (R): Acceleration a = −ω²x; when x > 0, a < 0, confirming the restoring nature of the force.

Assertion (A): The frequency of SHM of a spring-mass system increases if the spring constant is increased. Reason (R): Angular frequency ω = √(k/m); greater k gives greater ω and hence greater frequency ν = ω/2π.

Assertion (A): The function sin² ωt represents simple harmonic motion about equilibrium at x = 0. Reason (R): sin² ωt = ½ − ½ cos 2ωt, which is a periodic function with equilibrium at x = ½, not at x = 0.

Assertion (A): The projection of a particle undergoing uniform circular motion on the y-axis also executes SHM. Reason (R): The y-projection is y = A sin(ωt + φ), which is a sinusoidal function of time with the same amplitude and angular frequency as the x-projection.

Unlock all Assertion-Reason Questions

Practice in Quiz Mode