Motion in a Plane is a fundamental and high-weightage chapter in Class 11 Physics that introduces students to two-dimensional motion. This chapter explains important concepts such as scalars and vectors, vector addition and resolution, displacement, velocity, acceleration in two dimensions, uniform circular motion, and projectile motion, which form the base for advanced topics in mechanics.
NCERT Solutions for Class 11 Physics Chapter 3 – Motion in a Plane are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear vector diagrams and solved numericals, helping students develop strong conceptual clarity and problem-solving skills for school exams and competitive exams like JEE and NEET.
NCERT Solutions for Class 11 Physics Chapter 3 – Motion in a Plane
Q.
State, for each of the following physical quantities, if it is a scalar or a vector :
volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
Q.
A passenger arriving in a new town wishes to go from the station to a hotel located10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?
Q.
Read each statement below carefully and state, with reasons, if it is true or false:
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
Q.
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h, compare its centripetal acceleration with the acceleration due to gravity.
Q.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
Q.
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 ms-1 can go without hitting the ceiling of the hall?
Q.
In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
Q.
A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
Q.
Rain is falling vertically with a speed of 30 ms-1. A woman rides a bicycle with a speed of 10 ms-1 in the north to south direction. What is the direction in which she should hold her umbrella?
Q.
A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same speed how high above the ground can the cricketer throw the same ball?
Q.
Pick out the two scalar quantities in the following list :
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Q.
On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
Q.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge Pof the park, then cycles along the circumference, and returns to the centre along QOas shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement,(b) average velocity, and (c) average speed of the cyclist?
Q.
Three girls skating on a circular ice ground of radius200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. 4.20. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of path skate?
Q.
Q.
Q.
Read each statement carefully and state with reasons, if it is true or false:
(a) The magnitude of a vector is always a scalar.
(b) Each component of a vector is always a scalar.
(c) The total path length is always equal to the magnitude of the displacement vector of a particle
(d) The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time.
(e) Three vectors not lying in a plane can never add up to give a null vector.
Q.
State with reasons whether the following algebraic operations with scalars and vectors are meaningful:
(a) adding any two scalars
(b) adding a scalar to a vector of the same dimension
(c) multiplying any vector by any scalar
(d) multiplying any two scalars
(e) adding any two vectors
(f) adding a component of a vector to the same vector
Q.
Pick out the only vector quantity in the following list :
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
Q.
NCERT Solutions for Class 11 Physics Chapter 3 – Motion in a Plane
Q.1) State whether the following physical quantities are scalar or vector:
Volume, mass, speed, acceleration, density, number of moles, velocity,
angular frequency, displacement, angular velocity
Answer:
Scalar quantities: Volume, mass, speed, density, number of moles, angular frequency
Vector quantities: Acceleration, velocity, displacement, angular velocity
Q.2) Pick out the two scalar quantities from the following list:
Force, angular momentum, work, current, linear momentum, electric field,
average velocity, magnetic moment, relative velocity
Answer:
Work and current are scalar quantities.
Work is a scalar because it is the dot product of force and displacement.
Current is a scalar because it is described only by magnitude.
Q.3) Pick out the only vector quantity from the following list:
Temperature, pressure, impulse, time, power, total path length, energy,
gravitational potential, coefficient of friction, charge
Answer:
Impulse is the only vector quantity.
Impulse = change in momentum = force × time. Since force is a vector,
impulse is also a vector quantity.
Q.4) State whether the following operations are meaningful:
- Adding any two scalars
- Adding a scalar to a vector of same dimension
- Multiplying a vector by a scalar
- Multiplying any two scalars
- Adding any two vectors
- Adding a component of a vector to the same vector
Answer:
- No, unless both scalars represent the same physical quantity.
- No, a scalar cannot be added to a vector.
- Yes, for example velocity × time = displacement.
- Yes, multiplication of two scalars is meaningful.
- No, unless both vectors represent the same physical quantity.
- Yes, because both have the same dimensions.
Q.5) State whether the following statements are true or false:
- The magnitude of a vector is always a scalar.
- Each component of a vector is always a scalar.
- Total path length is always equal to displacement.
- Average speed is always greater than or equal to the magnitude of average velocity.
- Three non-coplanar vectors can never add up to give a null vector.
Answer:
- True. Magnitude of a vector is a pure number.
- False. Each component of a vector is also a vector.
- False. Path length ≥ displacement.
- True. Path length is always ≥ displacement.
- True. Non-coplanar vectors cannot form a closed triangle.
Q.6) State whether the following statements are true or false:
- The net acceleration in circular motion is always towards the centre.
- The velocity of a particle is always along the tangent to its path.
- The average acceleration over one cycle of uniform circular motion is zero.
Answer:
- False. This is true only in uniform circular motion.
- True. Velocity is always tangential to the path at any point.
- True. Acceleration direction keeps changing, so net vector over one cycle is zero.
Note: Q&A containing MathML / LaTeX may not render inside PDF.
FAQs: Class 11 Physics Chapter 3 – Motion in a Plane
Q1. Is Motion in a Plane important for exams?
Yes, it is a core mechanics chapter for Class 11 and competitive exams.
Q2. Which topics are most important in this chapter?
Vectors, projectile motion, and uniform circular motion.
Q3. Are numericals asked from this chapter?
Yes, projectile motion and vector-based numericals are very common.
Q4. Are diagrams important here?
Yes, vector and trajectory diagrams are frequently required.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals.