Chapter 3: Motion in a Plane Short Questions | physics Class 11 CBSE

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Chapter 3: Motion in a Plane Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Distinguish between a scalar quantity and a vector quantity with two examples each.

A scalar has magnitude only and follows ordinary algebra; examples are mass and temperature.
A vector has both magnitude and direction and obeys the triangle or parallelogram law of addition; examples are displacement and velocity.
The key distinction is that direction is associated with vectors but not with scalars.

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Question 2

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State the triangle law of vector addition and write its mathematical expression.

If two vectors are represented in magnitude and direction by two sides of a triangle taken in order, the third side taken in reverse order represents their resultant.
Mathematically, R = A + B, where R is represented by the closing side of the triangle formed by A and B placed head to tail.
The method is also called the head-to-tail method; the three vectors form three sides of a triangle.

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Question 3

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Show that vector addition is commutative.

When A and B are added head-to-tail (A then B), the resultant R points from tail of A to head of B.
When added in reverse order (B then A), the resultant R′ is identical in magnitude and direction to R.
Therefore A + B = B + A, proving commutativity of vector addition.

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Question 4

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What is a null vector? Give one physical example of its occurrence.

A null vector is a vector with zero magnitude; its direction cannot be specified.
It results from adding a vector to its negative: A + (−A) = 0.
Physically, if a particle moves from point P to P′ and returns to P, the net displacement is a null vector.

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Question 5

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Define a unit vector. Express a general vector A in terms of its unit vector.

A unit vector is a vector of unit magnitude pointing in a specific direction; it has no dimensions or units and is used only to specify direction.
The unit vector along A is n-hat = A/|A|.
Therefore, a vector A can be written as A = |A| n-hat.

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Question 6

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A vector A makes an angle θ with the x-axis. Write expressions for its x- and y-components and derive the magnitude of A.

The x-component is Ax = A cos θ and the y-component is Ay = A sin θ.
Since Ax² + Ay² = A²cos²θ + A²sin²θ = A²(cos²θ + sin²θ) = A².
Therefore |A| = √(Ax² + Ay²) and the direction is given by tan θ = Ay/Ax.

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Question 7

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If R = A + B, express the components of the resultant vector R in terms of the components of A and B.

Writing A = Ax i-hat + Ay j-hat and B = Bx i-hat + By j-hat, their sum is R = (Ax + Bx) i-hat + (Ay + By) j-hat.
Therefore Rx = Ax + Bx and Ry = Ay + By.
Each component of the resultant equals the algebraic sum of the corresponding components of the individual vectors.

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Question 8

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State the law of cosines for vector addition and write its formula.

When two vectors A and B enclose an angle θ, the magnitude of their resultant R is given by the law of cosines.
The formula is R = √(A² + B² + 2AB cos θ).
This result is derived from the parallelogram geometry using Pythagoras theorem applied to the component triangle.

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Question 9

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Define instantaneous velocity in two dimensions and state its direction.

Instantaneous velocity is the limiting value of average velocity as the time interval Δt approaches zero: v = lim(Δt→0) Δr/Δt = dr/dt.
It is expressed in component form as v = vx i-hat + vy j-hat, where vx = dx/dt and vy = dy/dt.
The direction of instantaneous velocity is always tangential to the path of motion at the given point.

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Question 10

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How is average acceleration defined for motion in a plane? Give its component form.

Average acceleration is defined as the change in velocity divided by the time interval: a-bar = Δv/Δt.
In component form: a-bar = (Δvx/Δt) i-hat + (Δvy/Δt) j-hat, giving components ax-bar = Δvx/Δt and ay-bar = Δvy/Δt.
Instantaneous acceleration a = dv/dt has components ax = dvx/dt and ay = dvy/dt.

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Question 11

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Write the equations of motion for a particle in a plane under constant acceleration, starting from rest at the origin.

With initial position r0 = 0 and initial velocity v0, the position at time t is r = v0t + (1/2)at².
In component form: x = voxt + (1/2)axt² and y = voyt + (1/2)ayt².
The velocity components are vx = vox + axt and vy = voy + ayt.

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Question 12

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State the key principle regarding the independence of motions in perpendicular directions for two-dimensional motion.

Motion in a plane with constant acceleration can be treated as two separate simultaneous one-dimensional motions along two perpendicular directions.
The x-direction motion and y-direction motion are completely independent of each other.
This principle, valid for constant acceleration, greatly simplifies analysis of projectile motion.

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Question 13

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Define a projectile and state the nature of acceleration acting on it after projection.

A projectile is any object that is in flight after being thrown or projected, such as a cricket ball or a football.
After projection, the only acceleration acting on the projectile is the acceleration due to gravity, g, directed vertically downward.
In component form: ax = 0 (no horizontal acceleration) and ay = −g.

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Chapter 3: Motion in a Plane | Short Questions

Distinguish between a scalar quantity and a vector quantity with two examples each.

State the triangle law of vector addition and write its mathematical expression.

Show that vector addition is commutative.

What is a null vector? Give one physical example of its occurrence.

Define a unit vector. Express a general vector A in terms of its unit vector.

A vector A makes an angle θ with the x-axis. Write expressions for its x- and y-components and derive the magnitude of A.

If R = A + B, express the components of the resultant vector R in terms of the components of A and B.

State the law of cosines for vector addition and write its formula.

Define instantaneous velocity in two dimensions and state its direction.

How is average acceleration defined for motion in a plane? Give its component form.

Write the equations of motion for a particle in a plane under constant acceleration, starting from rest at the origin.

State the key principle regarding the independence of motions in perpendicular directions for two-dimensional motion.

Define a projectile and state the nature of acceleration acting on it after projection.

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