NCERT / Physics / Ch.3

Motion in a Plane

Vectors · Projectile Motion · Relative Motion · Uniform Circular Motion
MCQ Master Series — 50 expert questions across 3 difficulty tiers.

⚡ Start Quiz 📊 Analytics
50
Questions
5
Topics
26
Concept Check (NCERT)
16
Boards / JEE Main Level
8
JEE/NEET Edge / HOTS
Question Intelligence

Quiz Analytics

A data-driven breakdown of all 50 questions by difficulty, exam origin and topic distribution.

📈 Distribution Overview

50
Total Questions
Concept Check (NCERT)
26
Boards / JEE Main Level
16
JEE/NEET Edge / HOTS
8

🗂 Topic Coverage

Vector Basics & Operations
28%
Projectile Motion (2D)
32%
Uniform Circular Motion
24%
Graph / Concept Applications
10%
Mixed 2D Motion & Relative
6%
26
Concept Check (NCERT)
16
Boards / JEE Main Level
8
JEE/NEET Edge / HOTS
Conceptual Framework

Key Concept Highlights

6 foundational pillars that power every question in this quiz. Understand these, and the answers follow naturally.

📐
Vectors in Two Dimensions
Physical quantities like displacement, velocity and force are represented by vectors, which combine magnitude with direction and can be added using component or parallelogram rules.
🧭
Components & Unit Vectors
Any vector in a plane can be resolved along perpendicular axes using unit vectors \( \mathbf{i}, \mathbf{j} \), making calculations with dot and cross products systematic and error‑free.
🎯
Projectile Motion in a Plane
Projectile motion is two‑dimensional motion under constant gravitational acceleration, with horizontal and vertical components treated independently using kinematic equations.
🌀
Uniform Circular Motion
In uniform circular motion, speed stays constant but velocity changes direction, producing centripetal acceleration and force directed toward the centre of the circular path.
✳️
Scalar & Vector Products
The scalar (dot) product relates vectors to work and projections, while the vector (cross) product gives area and perpendicular direction information, crucial for angle and perpendicularity tests.
📍
Position & Relative Motion
Position vectors locate particles in a plane and help describe relative motion, enabling analysis of paths when forces like gravity act or are suddenly removed.
Pedagogical Value

Why MCQs Matter

Multiple-choice questions are not mere guessing games — they are the sharpest diagnostic tool available to a competitive exam aspirant.

WHY
  • Force precise recall — vague conceptual understanding gets exposed immediately
  • Train elimination logic, a critical skill in JEE where partial knowledge suffices
  • Mirror CBSE Board objective and JEE Main Paper 1 formats exactly
  • Build decisive exam temperament — no room for hesitation
  • Reveal misconceptions that long-answer formats often mask
  • Provide instant feedback loops for targeted revision
~10–12%

of Class XI Mechanics weightage via vectors, projectile motion, relative motion in 2D and uniform circular motion in Boards & JEE/NEET.

Quick Reference

Important Formula Capsules

10 must-memorise equations that surface repeatedly across CBSE and JEE papers.

Vector Magnitude
\[ |\vec{A}| = \sqrt{A_x^2 + A_y^2} \]
Unit Vector
\[ \hat{A} = \dfrac{\vec{A}}{|\vec{A}|} \]
Dot Product
\[ \vec{A}\cdot\vec{B} = AB\cos\theta \]
Cross Product Magnitude
\[ |\vec{A}\times\vec{B}| = AB\sin\theta \]
Projectile – Time of Flight
\[ T = \dfrac{2u\sin\theta}{g} \]
Projectile – Range
\[ R = \dfrac{u^{2}\sin 2\theta}{g} \]
Projectile – Max Height
\[ H = \dfrac{u^{2}\sin^{2}\theta}{2g} \]
Centripetal Acceleration
\[ a_{c} = \dfrac{v^{2}}{r} = \omega^{2} r \]
Linear & Angular Speed
\[ v = \omega r \]
Angular Velocity
\[ \omega = \dfrac{2\pi}{T} \]
Learning Outcomes

What You Will Learn

By completing this quiz set you will have exercised all the following competencies.

01 Classify physical quantities as scalars or vectors and work confidently with unit vectors, components and geometric interpretation of vectors in a plane.
02 Compute magnitudes, directions, sums and differences of vectors using components, and decide when two vectors are equal, parallel or perpendicular via dot and cross products.
03 Apply projectile motion formulae for time of flight, range and maximum height, and understand the effect of launch angle, complementary angles and gravity on the trajectory.
04 Analyse uniform circular motion using relations between linear speed, angular speed, radius and centripetal acceleration, and identify directions of velocity, acceleration and centripetal force.
05 Relate dot products to angles and projections, and cross products to oriented areas and right‑hand‑rule directions in problems involving motion in two dimensions.
06 Interpret position vectors and argue qualitatively about paths when forces change or disappear, such as the motion of a projectile if gravity suddenly vanishes.
Exam Preparation

Strategy & Preparation Tips

5 evidence-based strategies to maximise your score in CBSE Boards and JEE.

01
Strategy
Master Vector Language First
Secure basics of unit vectors, components, magnitude and direction; nearly every MCQ in this chapter is easier once you translate the word problem into \(\mathbf{i},\mathbf{j}\) form.
02
Strategy
Projectile Templates on Autopilot
Memorise and practise using \(T, R, H\) formulae plus complementary‑angle properties so you can answer time‑of‑flight and range questions in seconds without re‑deriving.
03
Strategy
Think Direction in Circular Motion
For all circular motion items, immediately sketch radius, velocity and acceleration vectors; remember velocity is tangential, centripetal acceleration and force are radial inward.
04
Strategy
Use Dot & Cross as Concept Tests
Translate “perpendicular”, “parallel”, “maximum area” or “zero product” into conditions on \(\vec{A}\cdot\vec{B}\) and \(\vec{A}\times\vec{B}\); this quickly eliminates wrong options in vector MCQs.
05
Strategy
Check Limiting Cases & Units
When stuck, test extreme angles (0°, 45°, 90°) or speeds and verify units; correct dependence of R, H and \(a_c\) on \(u, \theta, r\) often reveals the right choice without full calculation.

Ready to Test Your Mastery?

50 questions  ·  Elapsed timer  ·  Instant scored results

⚡ Begin Motion in a Plane Quiz
🎯 Knowledge Check

Physics — MOTION IN A PLANE

50 Questions Class 11 MCQs
1
Which of the following quantities is a vector?
2
Two vectors are equal if they have the same
3
The magnitude of a unit vector is
4
The unit vector along the positive x-axis is denoted by
5
If \(\vec{A} = 3\mathbf{i} + 4\mathbf{j}\), its magnitude is
6
A vector making an angle \(90^\circ\) with x-axis has x-component equal to
7
Resolution of a vector means
8
In projectile motion, the horizontal acceleration is
9
The path followed by a projectile is
10
Time of flight of a projectile depends on
11
At the highest point of projectile motion, the vertical velocity is
12
For maximum range, the angle of projection is
13
Two complementary angles of projection give
14
In uniform circular motion, speed is
15
Direction of velocity in circular motion is
16
Centripetal acceleration is directed
17
Expression for centripetal acceleration is
18
Work done by centripetal force is
19
Angular velocity \(\omega\) is related to linear velocity by
20
Dimensional formula of angular velocity is
21
A projectile is thrown horizontally with speed \(u\). Its vertical velocity after time \(t\) is
22
If \(\vec{A} \cdot \vec{B} = 0\), the angle between them is
23
The scalar product of two vectors depends on
24
The magnitude of \(\vec{A} \times \vec{B}\) is maximum when angle is
25
Cross product of two parallel vectors is
26
The position vector of a particle gives information about
27
In projectile motion, acceleration is
28
A body moving in a circle with constant speed has acceleration because
29
For a given speed, which angle gives minimum range?
30
The area of triangle formed by vectors \(\vec{A}\) and \(\vec{B}\) is
31
If a particle completes one revolution in time \(T\), its angular velocity is
32
The horizontal range of a projectile is proportional to
33
A vector of zero magnitude is called
34
The dot product of two vectors gives
35
In uniform circular motion, centripetal force is always
36
A projectile has maximum time of flight for angle
37
If \(\vec{A} = \mathbf{i} + \mathbf{j}\) and \(\vec{B} = \mathbf{i} - \mathbf{j}\), then \(\vec{A}\cdot\vec{B}\) equals
38
The acceleration vector in circular motion is perpendicular to
39
If speed of circular motion doubles, centripetal acceleration becomes
40
For two vectors \(\vec{A}\) and \(\vec{B}\), if \(|\vec{A} + \vec{B}|\) is minimum, angle between them is
41
A projectile is fired upward with angle \(60^\circ\). Its horizontal velocity remains
42
The cross product of a vector with itself is
43
If radius of circular motion is halved keeping speed constant, centripetal acceleration becomes
44
A particle moves in a circle of radius \(r\) with angular speed \(\omega\). Its linear speed is
45
The maximum height of a projectile is proportional to
46
If \(\vec{A} \times \vec{B} = \vec{0}\), then vectors are
47
In circular motion, centripetal force is an example of
48
If gravity suddenly disappears, a projectile will move
49
The direction of \(\vec{A} \times \vec{B}\) is given by
50
In uniform circular motion, the velocity and acceleration vectors are
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Frequently Asked Questions

Motion in a plane is motion of a particle in two dimensions, where its position, velocity, and acceleration are represented by vectors in an \(x\text{-}y\) plane.

A scalar quantity is one that has only magnitude and no direction, such as mass, distance, speed, time, or temperature.

A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, and force.

Position vector \(\vec{r}\) of a particle at \((x,y)\) is given by \(\vec{r}=x\hat{i}+y\hat{j}\) with respect to the origin \(O(0,0)\).

Displacement vector is the change in position: \(\Delta\vec{r}=\vec{r}_2-\vec{r}_1\), independent of the actual path followed.

Average velocity is \(\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}\), where \(\Delta\vec{r}\) is displacement in time interval \(\Delta t\).

Instantaneous velocity is \(\vec{v}=\frac{d\vec{r}}{dt}\) and is always tangent to the path at that instant.

Average acceleration is \(\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}\), where \(\Delta\vec{v}\) is change in velocity in time \(\Delta t\).

Instantaneous acceleration is \(\vec{a}=\frac{d\vec{v}}{dt}\) and measures the rate of change of velocity vector at a given instant.

If two vectors are represented by two sides of a triangle taken in order, the third side taken in the same order represents their resultant.

If two vectors from the same point form adjacent sides of a parallelogram, the diagonal through that point gives the resultant vector.

For vectors \(\vec{A}\) and \(\vec{B}\) with angle \(\theta\) between them, resultant magnitude is \(R=\sqrt{A^2+B^2+2AB\cos\theta}\).

Vector subtraction \(\vec{A}-\vec{B}\) is defined as \(\vec{A}+(-\vec{B})\), where \(-\vec{B}\) has same magnitude as \(\vec{B}\) but opposite direction.

A unit vector has magnitude 1 and gives only direction; unit vector along \(\vec{A}\) is \(\hat{A}=\frac{\vec{A}}{|\vec{A}|}\)

If \(\vec{A}\) makes angle \(\theta\) with positive \(x\)-axis, then \(A_x=A\cos\theta\), \(A_y=A\sin\theta\), and \(\vec{A}=A_x\hat{i}+A_y\hat{j}\).

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