NEET/JEE Coaching Scholarship
ApplyGet up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
Ever wondered why a football moves in the air or why a car makes a turn on a curved road? Class 11 Physics Chapter 3 – Motion in a Plane tells you all about it through simple concepts such as projectile motion, circular motion, and vector addition. These Careers360 NCERT solutions make you understand each topic so clearly that you can write correct answers in exams confidently.
New: Get up to 90% Scholarship on NEET/JEE Coaching from top Coaching Institutes
New: JEE Main/NEET 2027 - Physics Important Formulas for Class 10
JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | Unacademy
NEET Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | ALLEN
To score good marks and better understanding in the Class 11 exams, it's important to practice the questions given at the end of each chapter in the NCERT book. Using the NCERT solutions available at Careers360, students will be able to frame relevant answers according to the syllabus.
NCERT solution for Class 11 Physics chapter 3 builds on the previous chapters, where we had learnt about motion in a straight line. Now, you will explore motion in a plane using concepts like position, velocity, and acceleration. These concepts are important for solving physics problems and will be useful in later chapters as well.
Download the NCERT solution for Class 11 Physics Chapter 3 Motion in a Plane –simple and clear answers to help you understand the chapter better and revise quickly.
Answer:
Volume is a scalar quantity since it has only magnitude without any direction.
Mass is a scalar quantity because it is specified only by magnitude.
Speed is specified only by its magnitude not by its direction so it is a scalar quantity .
Acceleration is a vector quantity as it has both magnitude and direction associated.
Density is a scalar quantity as it is specified only by its magnitude.
The number of moles is a scalar quantity as it is specified only by its magnitude.
Velocity is a vector quantity as it has both magnitude and direction.
Angular frequency is a scalar quantity as it is specified only by its magnitude.
Displacement is a vector quantity since it has both magnitude and associated direction.
Angular velocity is a vector quantity as it has both magnitude and direction.
Q. 3.2 Pick out the two scalar quantities in the following list :
Answer:
The two scaler quantities are work and current , as these two don't follow laws of vector addition.
Q. 3.3 Pick out the only vector quantity in the following list :
Answer:
Among all, the impulse is the only vector quantity as it is the product of two vector quantities. Also, it has an associated direction.
Answer:
(a) Adding two scalars is meaningful if the two have the same unit or both represent the same physical quantity.
(b) Adding a scalar to a vector of the same dimensions is meaningless as vector quantity has associated direction.
(c) Multiplication of vector with scaler is meaningful as it just increases the magnitude of vector quantity and direction remains the same.
(d) Multiplication of scaler is valid and meaningful , unbounded of any condition. This is because, if we have two different physical quantity then their units will also get multiplied.
(e) Adding two vectors is meaningful if they represent the same physical quantity. This is because their magnitude will get added and direction will remain the same.
(f) Adding a component of a vector to the same vector is meaningful as this represents the same case of adding vectors with the same dimensions. In this, the magnitude of the resultant vector will increase and the direction will remain the same.
Q. 3.5 Read each statement below 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 the 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.
Answer:
(a) True.
Since the magnitude of a vector will not have any direction (also it is a number), so it will be scaler.
(b) False.
The component of a vector will always be a vector as it will also have a direction specified.
(c) False.
This is true only in case when the particle is moving in a straight line. This is because path length is a scalar quantity whereas displacement is vector.
(d) True
From the above part (c) it is clear that total path length is either equal or greater than the displacement. As a result given statement is true.
(e) True
Since they don't lie in the same plane so they cannot give null vector after addition.
Q. 3.6 (a) Establish the following vector inequalities geometrically or otherwise :
( a)
Answer:
Consider the image given below :-
In
or
But if
From (i) and (ii), we can conclude that,
Q. 3.6 (b) Establish the following vector inequalities geometrically or otherwise :
(b)
Answer:
Consider the given image:
In
Sum of two sides of a triangle is greater than the length of another side.
or
or
or
Also, if
From (i) and (ii), we get :
Q. 3.6 (c) Establish the following vector inequalities geometrically or otherwise :
(c)
Answer:
Consider the image given below:-
In
or
For vectors in a straight line,
From (i) and (ii) we get :
Q. 3.6 (d) Establish the following vector inequalities geometrically or otherwise :
(d)
Answer:
Consider the image given below :
In
or
or
Also, if the vectors are in a straight line then :
From (i) and (ii), we can conclude :
Q. 3.7 Given a + b + c + d = 0, which of the following statements are correct:
(a) a, b, c, and d must each be a null vector,
(b) The magnitude of (a + c) equals the magnitude of ( b + d),
(c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d,
(d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
Answer:
(a) Incorrect: - Sum of three vectors in a plane can be zero. So it is not a necessary condition that all of a,b,c,d should be null vector.
(b) Correct : We are given that a + b + c + d = 0
So, a + b = - (c + d)
Thus magnitude of a + c is equal to the c+d.
(c) Correct :- We have a + b + c + d = 0
b + c + d = - a
So clearly magnitude of a cannot be greater than the sum of the other three vectors.
(d) Correct: - Sum of three vectors is zero if they are coplanar.
Thus, a + b + c + d = 0
or a + (b + c) + d = 0
Hence (b+c) must be coplaner with a and d
Answer:
The displacement vector is defined as the shortest distance between two points which particle had covered.
In this case, the shortest distance between these points is the diameter of the circular ice ground.
Thus, Displacement = 400 m.
Girl B had travelled along the diameter so path travelled by her is equal to the displacement.
(a) net displacement,
Answer:
The net displacement, in this case, will be zero because the initial and final position is the same.
Net displacement = Final position - Initial position .
(b) average velocity,
Answer:
(b) Average velocity is defined as the net displacement per unit time. Since we have the net displacement to be zero so the avg. velocity will also be zero .
(c) the average speed of the cyclist?
Answer:
(c) For finding average speed we need to calculate the total path travelled.
Total path = OP + arc PQ + OQ
So the avg. speed is :
Answer:
The track is shown in the figure given below:-
Let us assume that the trip starts at point A.
The third turn will be taken at D.
So displacement will be = Distance AD = 500 + 500 = 1000 m
Total path covered = AB + BC + CD = 500 + 500 + 500 = 1500 m
The sixth turn is at A.
So the displacement will be Zero
and total path covered will be = 6 (500) = 3000 m
The eighth turn will be at C.
So the displacement = AC
or
And the total distance covered = 3000 + 1000 = 4000 m=4Km
(a) the average speed of the taxi,
Answer:
(a) Avg. speed of taxi is given by:-
(b) the magnitude of average velocity? Are the two equal?
Answer:
Total displacement = 10 Km
Total time taken in hours :
Avg. velocity :
It can be clearly seen that avg. speed and avg. velocity is not the same.
Answer:
It is known that the maximum height reached by a particle in projectile motion is given by :
Putting the given values in the above equation :
So, we get
Now the horizontal range can be found from :
or
Answer:
We are given the range of projectile motion.
Substituting values :
So,
Now since deacceleration is also acting on the ball in the downward direction :
Since final velocity is 0, so maximum height is given by :
or
Answer:
Frequency is given by :
And, the angular frequency is given by :
Thus,
Hence the acceleration is given by :
or
or
Answer:
Convert all the physical quantities in SI units.
So the acceleration is given by :
The ratio of centripetal acceleration with gravity gives :
Q. 3.16 (a) Read each statement below carefully and state, with reasons, if it is true or false :
Answer:
False :- Since the net acceleration is not directed only along the radius of the circle. It also has a tangential component.
Q. 3.16 (b) Read each statement below carefully and state, with reasons, if it is true or false :
Answer:
True: - Because particle moves on the circumference of the circle, thus at any its direction should be tangential in order to move in a circular orbit.
Q. 3.16 (c) Read each statement below carefully and state, with reasons, if it is true or false :
Answer:
True: - In a uniform circular motion, acceleration is radially outward all along the circular path. So in 1 complete revolution, all the vectors are cancelled and the null vector is obtained.
(a) Find the
Answer:
(a) We are given the position vector
The velocity vector is given by:-
or
Now for acceleration :
(b) What is the magnitude and direction of velocity of the particle at
Answer:
Put the value of time t = 2 in the velocity vector as given below :
or
or
Thus the magnitude of velocity is :
Direction :
(a) At what time is the x- coordinate of the particle
Answer:
We are given the velocity of the particle as
And the acceleration is given as :
So, the velocity due to acceleration will be :
So,
By integrating both sides,
or
Here u is the initial velocity (at t = 0 sec).
Now,
or
Integrating both sides, we get
or
or
Comparing coefficients, we get :
In the question, we are given x = 16.
So t = 2 sec
and y = 10 (2) + 2 2 = 24 m.
(b) What is the speed of the particle at the time?
Answer:
The velocity of the particle is given by :
Put t = 2 sec,
So velocity becomes :
or
Now, the magnitude of velocity gives :
Answer:
Let A be a vector such that:-
Then the magnitude of vector A is given by :
Now let us assume that the angle made between vector A and x-axis is
Then we have:-
Similarly, let B be a vector such that:-
The magnitude of vector B is :
Let
Now consider
Then the required components of a vector C along the directions of
and the required components of a vector C along the directions of
Q. 3.20 For any arbitrary motion in space, which of the following relations are true :
(a)
(b)
(c)
(d)
(e)
Answer:
(a) False:- Since it is arbitrary motion so the following relation cannot hold all the arbitrary relations.
(b) True:- This is true as this relation relates displacement with time correctly.
(c) False: - The given equation is valid only in case of uniform acceleration motion.
(d) False:- The given equation is valid only in case of uniform acceleration motion. But this is arbitrary motion so acceleration can be no-uniform.
(e) True:- This is the universal relation between acceleration and velocity-time, as the definition of acceleration is given by this.
Q. 3.21 Read each statement below carefully and state, with reasons and examples, if it is true or false :
A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space (e) has the same value for observers with different orientations of axe
Answer:
(a) False:- For e.g. energy is a scalar quantity but is not conserved in inelastic collisions.
(b) False:- For example temperature can take negative values in degree Celsius.
(c) False:- Since speed is a scalar quantity but has dimensions.
(d) False:- Gravitational potential varies in space from point to point.
(e) True:- Since it doesn't have direction.
Answer:
The given situation is shown in the figure:-
For finding the speed of aircraft we just need to find the distance AC as we are given t = 10 sec.
Consider
or
or
or
Thus, the speed of aircraft :
Answer:
The given situation is shown in the figure:-
Since both rain and woman are having some velocity so we need to find the relative velocity of rain with respect to woman.
And the angle is given by :
Hence woman needs to hold an umbrella at 18 degrees from vertical towards the south.
Answer:
The speed of man is (swim speed ) = 4 Km/h.
Time taken to cross the river will be :
Total distance covered due to the flow of the river:-
Answer:
According to the question the figure is shown below:-
The angle between velocity of wind and opposite of velocity of boat is (90 + 45) = 135 degree.
Using geometry,
Thus
So the flag will be just 0.11 degree from the perfect east direction.
Answer:
No, a vector doesn't have a definite location as a vector can be shifted in a plane by maintaining its magnitude and direction.
Vector can change with time for e.g. displacement vector.
No, two equal vectors at a different locations may not have identical physical effects. For e.g., two equal force vectors at a different location may have different torque but when they are applied together the net torque would be different.
Answer:
The main condition for a physical quantity to be a vector is that it should the law of vector addition. Also, the vector has both direction and, magnitude but these are not sufficient condition. For e.g. current has both magnitude and direction but is a scalar quantity as it doesn't follow the law of vector addition.
Rotation is not a vector on a large basis, as it is measured by an angle which follows the law of scaler addition.
Q.6(a)_Can you associate vectors with (a) the length of a wire bent into a loop, Explain.
Answer:
No, the length of a wire bent into a loop cannot be expressed in vector form as we have no direction associated with it.
Q.6(b) Can you associate vectors with (b) a plane area, Explain.
Answer:
The plane area can be expressed in vector form as direction can be associated as pointing outward or inward (normal to the plane) of the area.
Q. 6(c) Can you associate vectors with (c) a sphere? Explain.
Answer:
No, vector cannot be associated with a sphere as direction cannot be associated with sphere anyhow.
Answer:
The range of bullet is given to be:- R = 3 Km.
or
or
Now, we will find the maximum range (maximum range occurs when the angle of projection is 45 0 ).
or
Thus the bullet cannot travel up to 5 Km.
Answer:
According to the question the situation is shown below:-
Now, the horizontal distance traveled by the shell = Distance traveled by plane
or
or
or
So,
So, the required height will be:-
or
or
or
Answer:
Speed of cycle = 27 Km/h = 7.5 m/s
The centripetal acceleration is given by :
And the tangential acceleration is given as
So, the net acceleration becomes :
or
or
Now for direction,
or
Thus,
where the symbols have their usual meaning.
Answer:
Using the equation of motion in both horizontal and vertical direction.
Now,
or
Thus,
Q.11 Shows that the projection angle
where the symbols have their usual meaning.
Answer:
(b) The maximum height is given by :
And, the horizontal range is given by :
Dividing both, we get :
Hence
Q1. A body is projected at t= 0 with a velocity 10ms-1 at an angle of 600 with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms-2, the value of R (in meters) is:
a) 2.8
b)10.3
c)2.5
d)5.1
Answer:
We know that,
Now, calculating speed at
Hence, the answer is the option(1).
Q.2. The maximum speed of a boat in still water is
(Take
a) 2000
b)3000
c)4000
d)5000
Answer:
Hence, the answer is the option (1).
Q.3 Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is 30o and its maximum height is then the maximum height of the other will be
Answer:
Given: One ball's projection angle is
Explanation:
The question tells us that the range is equal, so the angles of projection must be complementary for the range to be equal.
Now, let us consider the angle of projection of one ball is
By using known values in the formula, we can now determine the maximum range of each ball.
Now, for the second ball
Hence, the maximum height of others will be 3 h
Hence, the answer is 3h.
Q 4. swimmer crosses the river along the line making an angle of 45º with the direction of flow. The velocity of the river is 5 m/s. A swimmer takes 6 seconds to cross the river of width 60 m. The velocity of the swimmer with respect to water will be:
Answer:
River flow along y direction with a velocity of 5 j m/s.
The swimmer crossover along the vector: i + j since the angle is 45 degree
displacement of swimmer just after crossing = 60 i + 60 j meters
speed of the swimmer with respect to a stationary observer
= (60 i + 60 j) / 6 m/s = 10 i + 10 j m/s
velocity of swimmer relative to the river = 10 i + 10 j - 5 j
magnitude of velocity relative to river = 5√5 m/s
Hence, the answer is 5√5.
Q 5. A man wearing a hat of extended length 12 cm is running in rain falling vertically downwards with a speed of 10 m/s. The maximum speed with which man can run, so that raindrops do not fall on his face (the length of his face below the extended part of the hat is 16 cm) will be : (please give your answer in m/s)
Answer:
for Rain - Man Problem -
respect to man makes with the vertical
- wherein
Let, the velocity of
then,
For the required conditions:
Hence, the answer is 7.5.
| ||
|
| |
|
|
|
|
|
|
|
| |
|
|
|
|
|
|
|
| |
|
|
|
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
|
|
|
The Topic and Subtopic of Physics Chapter 3 Class 11 are listed below.
Section Name |
Topic Name |
3 | |
3.1 |
Introduction |
3.2 | |
3.3 |
Multiplication of Vectors by Real Numbers |
3.4 |
Addition and Subtraction of Vectors - Graphical Method |
3.5 |
Resolution of Vectors |
3.6 |
Vector addition — analytical method |
3.7 |
Motion in a plane |
3.8 |
Motion in a plane with constant acceleration |
3.9 | |
3.10 |
Chapter 3 of NCERT Class 11 Physics is important for exams as it carries high marks and covers key concepts like vectors, relative velocity, circular motion, and projectile motion in detail. To score well, students should have a strong grasp of the concepts and formulas discussed in this chapter.
This chapter covers vectors, their addition and resolution, motion in two dimensions, projectile motion, uniform circular motion, and relative velocity.
Resistance is the opposition to the flow of electric current in a wire or device. It depends on the length, thickness, and type of material. Resistivity, on the other hand, is a property of the material itself. It tells how much a material resists current flow, no matter its size or shape.
Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide