NCERT Solutions Class 11 Physics Chapter 3 Motion in a Plane

The Class 11 Physics NCERT Solutions Chapter 3 Motion in a Plane will help students prepare for Boards, JEE Main, JEE Advanced, NEET, CUET and NDA in 2026-27. Every back-exercise question is solved with full working, so students can check each vector addition, resolution, projectile numerical, and circular-motion step by step.

This chapter takes the motion ideas from a straight line and extends them to two dimensions using vectors.

• CBSE Weightage: 6 to 8 marks, usually one numerical on projectile motion plus one short answer on vectors.
• Questions solved: all Exercise 3.1 onward, covering scalars and vectors, vector addition, projectile motion, and circular motion.
• Key formulas: range, maximum height, time of flight, and centripetal acceleration.

Each solution in this Class 11 Physics NCERT Solutions Chapter 3 Motion in a Plane compilation is curated by subject experts, based on the 2026-27 NCERT textbook, and refined against the last five years of CBSE Board, JEE Main and NEET papers.

Scalars and Vectors in Motion in a Plane

Motion in two dimensions needs a quantity that carries direction. The chapter starts by sorting every physical quantity into two groups. Getting this split right is the first step in solving any numerical here, because the maths for each group is different.

The NCERT questions here ask students to name whether a quantity is a scalar or a vector and to add them the right way. Scalars add by simple arithmetic, but vectors add by the triangle or parallelogram law. The solved answers state which rule applies before any number goes in. This habit stops the most common early error in the chapter, which is adding two vectors as if they were plain numbers.

Vector Addition: Triangle Law and Parallelogram Law

Two vectors are combined into a single resultant using one of two laws. Both give the same answer, and the NCERT solutions pick whichever fits the question. The parallelogram law also gives a formula for the size of the resultant, which the numericals use often.

• Triangle law: draw the second vector from the tip of the first; the resultant runs from the start of the first to the tip of the second.
• Parallelogram law: draw both vectors from the same point; the diagonal of the parallelogram is the resultant.
• Magnitude of the resultant: R = √(A² + B² + 2AB cos θ), where θ is the angle between the two vectors.

Several numericals, such as Exercise 3.1, ask students to find the resultant of two forces or velocities. The method is fixed: write the two magnitudes, read off the angle between them, then use the formula. Vector addition is commutative, so A + B = B + A, but subtraction is not. The Class 11 Physics NCERT Solutions Chapter 3 Motion in a Plane show the angle on its own line so no step is skipped.

Resolution of Vectors and Unit Vectors

The reverse of addition is resolution, which splits one vector into parts along chosen axes. Breaking a vector into its x and y components turns a two-dimensional problem into two simple one-dimensional problems. The NCERT answers use this trick in almost every projectile numerical.

• A vector A at angle θ has components A_x = A cos θ and A_y = A sin θ.
• The unit vectors i, j, k point along the x, y and z axes and each have a magnitude of one.
• Any vector is written as A = A_x i + A_y j in component form.

Questions like Exercise 3.10 give a vector and ask for its components, or give the components and ask for the magnitude and direction. Always resolve every vector into x and y parts before adding them. Once in component form, the x-parts add together and the y-parts add together, which is far safer than drawing diagrams. The solved answers keep the two axes in separate columns so students never mix them.

Projectile Motion: Range, Maximum Height and Time of Flight

A projectile is any object thrown at an angle that then moves only under gravity. Its path is a parabola. The chapter treats the horizontal and vertical motions on their own, and the NCERT solutions solve every projectile numerical with the three standard formulas below.

Numericals such as Exercise 3.14 give the launch speed and angle and ask for the range or the height. The range is largest when the launch angle is 45 degrees, because sin 2θ reaches its maximum value of one there. The horizontal velocity stays constant through the whole flight, while only the vertical velocity changes. The solved answers split the two motions clearly, which is exactly how CBSE expects the working to be shown.

Uniform Circular Motion and Centripetal Acceleration

An object moving in a circle at steady speed is in uniform circular motion. Its speed does not change, but its direction changes at every instant, so it is always accelerating. This acceleration points towards the centre and is called centripetal acceleration.

• Centripetal acceleration: a = v² / r, directed towards the centre of the circle.
• In terms of angular speed: a = ω² r, where ω is the angular speed.
• Link between the two: v = r ω, so a larger radius means a larger linear speed for the same turning rate.

Questions like Exercise 3.18 ask for the acceleration of a car on a curve or a stone on a string. In uniform circular motion the speed is constant but the velocity is not, because direction keeps changing. This point catches many students, so the solved answers state it before the calculation. Centripetal acceleration is a favourite topic for JEE Main and NEET objective questions.

Exercise-wise Breakdown for Class 11 Physics Chapter 3 Motion in a Plane

The NCERT back-exercise splits into clear groups. Use this map to plan which answers to practise first for the 2026-27 boards. Every group links to the full solved set.

Solving the groups in this order builds the skills in the same sequence the chapter teaches them. Start with vector basics, then resolution, then projectile and circular motion, because each group uses the one before it.

Common Mistakes Students Make in the Motion in a Plane Chapter

These slips happen while writing or calculating the answer, not because the concept is unclear. Each one costs 1 to 3 marks in the CBSE paper, so the solved answers point them out at the exact step.

Student Feedback on the Motion in a Plane Chapter

Practice Questions for Class 11 Physics Chapter 3 Motion in a Plane

Once the solved answers are clear, test yourself on the full question set. The practice page has every NCERT question with a step-by-step Solution and an Expert Solution behind a click.

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