Chapter 3: Motion in a Plane Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 1

Logic Check

Assertion (A): The displacement vector of an object does not depend on the path taken between two points. Reason (R): Displacement is defined as the straight-line vector from the initial position to the final position.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 2

Logic Check

Assertion (A): Vector addition is commutative, i.e., A + B = B + A. Reason (R): Vector addition is also associative, i.e., (A + B) + C = A + (B + C).

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 3

Logic Check

Assertion (A): The magnitude of the sum of two vectors can never exceed the sum of their individual magnitudes. Reason (R): The resultant magnitude R = √(A² + B² + 2AB cos θ), which is maximum when θ = 0° and equals A + B.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 4

Logic Check

Assertion (A): A null vector has zero magnitude and its direction cannot be specified. Reason (R): A null vector results when a vector is added to its negative.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 5

Logic Check

Assertion (A): The instantaneous velocity of a particle is always directed tangentially to its path at that point. Reason (R): As the time interval Δt approaches zero, the displacement Δr aligns with the tangent to the path.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 6

Logic Check

Assertion (A): In projectile motion, the horizontal component of velocity remains constant throughout the flight. Reason (R): There is no acceleration component along the horizontal direction (air resistance neglected).

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 7

Logic Check

Assertion (A): The path of a projectile is always a parabola. Reason (R): The x-coordinate of a projectile is a linear function of time while the y-coordinate is a quadratic function of time.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 8

Logic Check

Assertion (A): The total time of flight of a projectile is twice the time to reach maximum height. Reason (R): The upward and downward parts of the parabolic path are symmetric about the highest point.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 9

Logic Check

Assertion (A): The horizontal range of a projectile is maximum when the angle of projection is 45°. Reason (R): At 45°, sin 2θ0 = sin 90° = 1, which is the maximum value of sin 2θ0.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 10

Logic Check

Assertion (A): Centripetal acceleration is not a constant vector. Reason (R): The magnitude of centripetal acceleration changes continuously in uniform circular motion.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 11

Logic Check

Assertion (A): In uniform circular motion, the speed of an object is constant but its velocity is not. Reason (R): The direction of velocity in uniform circular motion changes continuously.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 12

Logic Check

Assertion (A): Kinematic equations for uniform acceleration (v = v0 + at, etc.) cannot be applied to uniform circular motion. Reason (R): In uniform circular motion, the magnitude of acceleration is zero.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 13

Logic Check

Assertion (A): The average velocity of a particle can be zero even when its average speed is non-zero. Reason (R): Average velocity depends on displacement while average speed depends on total path length.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 14

Logic Check

Assertion (A): A unit vector has magnitude 1 and is dimensionless. Reason (R): A unit vector is used to specify the direction of a vector and carries no physical dimension.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 15

Logic Check

Assertion (A): For two projectiles launched with the same initial speed, the one at 30° and the one at 60° have equal horizontal ranges. Reason (R): sin 2(30°) = sin 60° = sin 2(60°) = sin 120°, and both equal √3/2.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 16

Logic Check

Assertion (A): The magnitude of displacement of an object is always equal to its path length. Reason (R): Displacement is the shortest distance between initial and final positions.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 17

Logic Check

Assertion (A): In two-dimensional motion with constant acceleration, the motions along x and y directions are independent of each other. Reason (R): The acceleration components ax and ay can be treated separately and do not influence each other.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 18

Logic Check

Assertion (A): The velocity vector at a point on the circular path and the radius vector at that point are always perpendicular. Reason (R): In uniform circular motion, speed is constant, so no tangential acceleration exists, and velocity is purely tangential.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 19

Logic Check

Assertion (A): A vector quantity can be multiplied by a scalar having its own physical dimension. Reason (R): The result of such multiplication is a new vector with dimensions equal to the product of the scalar's and the original vector's dimensions.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 20

Logic Check

Assertion (A): At the maximum height of a projectile, the speed is zero. Reason (R): At maximum height, the vertical component of velocity is zero but the horizontal component remains unchanged.

Reasoning Options

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Chapter sections

Chapter 3: Motion in a Plane | Assertion-Reason

Assertion (A): The displacement vector of an object does not depend on the path taken between two points. Reason (R): Displacement is defined as the straight-line vector from the initial position to the final position.

Assertion (A): Vector addition is commutative, i.e., A + B = B + A. Reason (R): Vector addition is also associative, i.e., (A + B) + C = A + (B + C).

Assertion (A): The magnitude of the sum of two vectors can never exceed the sum of their individual magnitudes. Reason (R): The resultant magnitude R = √(A² + B² + 2AB cos θ), which is maximum when θ = 0° and equals A + B.

Assertion (A): A null vector has zero magnitude and its direction cannot be specified. Reason (R): A null vector results when a vector is added to its negative.

Assertion (A): The instantaneous velocity of a particle is always directed tangentially to its path at that point. Reason (R): As the time interval Δt approaches zero, the displacement Δr aligns with the tangent to the path.

Assertion (A): In projectile motion, the horizontal component of velocity remains constant throughout the flight. Reason (R): There is no acceleration component along the horizontal direction (air resistance neglected).

Assertion (A): The path of a projectile is always a parabola. Reason (R): The x-coordinate of a projectile is a linear function of time while the y-coordinate is a quadratic function of time.

Assertion (A): The total time of flight of a projectile is twice the time to reach maximum height. Reason (R): The upward and downward parts of the parabolic path are symmetric about the highest point.

Assertion (A): The horizontal range of a projectile is maximum when the angle of projection is 45°. Reason (R): At 45°, sin 2θ0 = sin 90° = 1, which is the maximum value of sin 2θ0.

Assertion (A): Centripetal acceleration is not a constant vector. Reason (R): The magnitude of centripetal acceleration changes continuously in uniform circular motion.

Assertion (A): In uniform circular motion, the speed of an object is constant but its velocity is not. Reason (R): The direction of velocity in uniform circular motion changes continuously.

Assertion (A): Kinematic equations for uniform acceleration (v = v0 + at, etc.) cannot be applied to uniform circular motion. Reason (R): In uniform circular motion, the magnitude of acceleration is zero.

Assertion (A): The average velocity of a particle can be zero even when its average speed is non-zero. Reason (R): Average velocity depends on displacement while average speed depends on total path length.

Assertion (A): A unit vector has magnitude 1 and is dimensionless. Reason (R): A unit vector is used to specify the direction of a vector and carries no physical dimension.

Assertion (A): For two projectiles launched with the same initial speed, the one at 30° and the one at 60° have equal horizontal ranges. Reason (R): sin 2(30°) = sin 60° = sin 2(60°) = sin 120°, and both equal √3/2.

Assertion (A): The magnitude of displacement of an object is always equal to its path length. Reason (R): Displacement is the shortest distance between initial and final positions.

Assertion (A): In two-dimensional motion with constant acceleration, the motions along x and y directions are independent of each other. Reason (R): The acceleration components ax and ay can be treated separately and do not influence each other.

Assertion (A): The velocity vector at a point on the circular path and the radius vector at that point are always perpendicular. Reason (R): In uniform circular motion, speed is constant, so no tangential acceleration exists, and velocity is purely tangential.

Assertion (A): A vector quantity can be multiplied by a scalar having its own physical dimension. Reason (R): The result of such multiplication is a new vector with dimensions equal to the product of the scalar's and the original vector's dimensions.

Assertion (A): At the maximum height of a projectile, the speed is zero. Reason (R): At maximum height, the vertical component of velocity is zero but the horizontal component remains unchanged.

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