NCERT Solution (Class 11) > Physics Chapter 4 Motion In A Plane
NCERT Solution Class 11 Physics Chapter 4 Motion In A Plane: National Council of Educational Research and Training Class 11 Physics Chapter 4 Solution – Motion In A Plane. Free PDF Download facility available at our website.
Board |
NCERT |
Class |
11 |
Subject |
Physics |
Chapter |
4 |
Chapter Name |
Motion In A Plane |
Topic |
Exercise Solution |
Motion In A Plane Chapter all Questions and Numericals Solution
4.1) 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.
ANSWER-
A scalar quantity has magnitude only. It does not have any direction.
A vector quantity has magnitude as well as the direction.
Scalar: Volume, mass, speed, density, number of moles, angular frequency.
Vector: Acceleration, velocity, displacement, angular velocity.
4.2) 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.
ANSWER-
Work and current.
We know that Work done is the dot product of force and displacement. Since the dot product is always a scalar quantity hence work is also scalar quantity.
Current does not follow law of vector addition hence it is considered as scalar quantity.
4.3) 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.
ANSWER-
Impulse
Impulse is defined as the product of force and time. We know that force is a vector quantity and time is a scalar quantity and we know that product of vector with scalar gives vector quantity hence the impulse is vector quantity.
4.4) State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(a) Adding any two scalars, (b) adding a scalar to a vector of the same dimensions , (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.
ANSWER-
(a) Meaningful. The addition of two scalar quantities is meaningful only if they both represent the same physical quantity. Like we can add one distance with other distance but we cant add one distance and other speed even though both are scalars because they do not represents same physical quantity.
(b) not Meaningful. The addition of a vector quantity with a scalar quantity is not meaningful.
(c) Meaningful. A scalar can be multiplied to any vector.
(d) Meaningful. One scalar can be multiplied to other scalar no matter whether they represents same or different physical quantity.
(e) Meaningful. The addition of two vector quantities is meaningful only if they both represent the same physical quantity. Like we can add force with other force but we cant add one force and other impulse even though both are vectors because they do not represents same physical quantity.
(f) Meaningful. A component of a vector can be added to the same vector as they both are vectors and represents same physical quantity.
4.5) 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 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.
(a) True. Magnitude of any vector is represented by any number hence it is scalar.
(b) False. Any vector can be resolved into components which are also the vectors only and not the scalar.
(c) False. Total path length is the distance covered by by body while displacement is the shortest distance between start and end point so total path length is always either greater than or equal to displacement.
(d) True. as total path length is is always greater than or equal to displacement. Hence the derived quantity from path length i.e. speed is always either greater or equal to the magnitude of average velocity of the particle over given time interval.
(e) True. Three vectors not lying in a plane cannot cancels each other hence can never add up to give a null vector.
4.6)
4.7) 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-
Given a + b + c + d = 0.
a) Not correct. To get a + b + c + d = 0 there is no need to have all vectors to be null vectors there are many combinations where all vectors cancels each others components and gives the result of 0.
b) Correct
a + b + c + d = 0
a + c = – b – d
a + c = – (b + d)
taking magnitude only we can say
| a + c | = | – (b + d)| = | b + d |
The magnitude of (a + c) equals the magnitude of ( b + d).
c) Correct
a + b + c + d = 0
∴ a = – ( b + c + d )
taking magnitude only we can say
∴ | a| = |( b + c + d )|
∴ | a| ≤ | b|+| c|+|d|
Hence magnitude of a should be less than or equal to sum of the magnitudes of b, c, and d.
d) Correct
a + (b + c) + d = 0
the sum of three vectors a ,(b + c) and d can be zero only if all lie in same plane three vectors are represented by the three sides of a triangle.
If a and d are not collinear then b + c must lie in the line of a and d.
4.10)
4.11)
4.12)
4.13)
4.14)
4.15)
In case you are missed :- Previous Chapter Solution
4.17)
4.18)
4.19) 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 vector 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
ANSWER-
(a) False. The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre in case of uniform circular motion only. In case of not uniform circular motion there is two components of accelerations one is along the radius called centripetal acceleration and other is called tangential acceleration.
(b) True.it is a fact that The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) True. The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector because its magnitude is constant but direction vector always changes and cancels each other during one complete cycle gives null vector.
4.20)
4.21)
4.22) i and j are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors i + j, and i − j ?
ANSWER-
Vector A is given by,
A = xi + y j
4.23) For any arbitrary motion in space, which of the following relations are true:
(a) vaverage= (1/2) (v (t1) + v (t2))
(b) vaverage = [r (t2) – r(t1) ] /(t2 – t1)
(c) v(t) = v (0) + a t
(d) r(t) = r (0) + v (0) t + (1/2) a t2
(e) aaverage= [v(t2) – v (t1)] /(t2 – t1)
(The ‘average’ stands for average of the quantity over the time interval t1 to t2)
ANSWER-
(a) given equation is for particular case but as a given motion is arbitrary in space hence average velocity can’t be expressed by given equation.
(b) given equation is general equation which represent any motion hence given arbitrary motion can be represented by equation.
(c) v(t) = v (0) + a t. This equation is for uniform acceleration motion but given motion is arbitrary motion which can be non-uniform acceleration motion hence given motion cannot be represented by given equation.
(d) r (t) = r (0) + v (0) t + (1/2) at2 .This equation is for uniform acceleration motion but given motion is arbitrary motion which can be non-uniform acceleration motion hence given motion cannot be represented by given equation.
(e) given equation is general equation which represent any motion hence given arbitrary motion can be represented by equation.
4.24) 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 axes.
ANSWER-
(a) False. If we considered inelastic collision where kinetic energy is not conserved even if it is scalar quantity hence given statement is not true.
(b) False. Temperature can be negative even though it is scalar quantity.
(c) False. Speed is scalar quantity but it has unit of meter per second.
(d) False. Gravitational potential energy vary point to point even though it is scalar.
(e) True. scalars do not change with frame of reference.
4.25)
Additional Exercises
4.26) A vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors a and b at different locations in space necessarily have identical physical effects? Give examples in support of your answer.
ANSWER-
A vector has no definite locations in space because its magnitude and direction remain the same if location changes.
A vector can vary with time.
Two equal vectors located at different locations in space need not produce the same physical effect.
4.27) A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?
ANSWER-
A physical quantity having both magnitude and direction is not necessarily a vector.
The rotation of a body about an axis is not a vector quantity even though it has magnitude and direction as it does not follow the law of vector addition. However, a rotation by a certain small angle follows the law of vector addition and is therefore considered a vector.
4.28) Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.
ANSWER-
(a) NO. We can’t associate vectors with length of wire as it is a scalar in nature.
(b) Yes. We can associate vector to the plane area with direction normal to the cross section.
(c) Yes. We can associate vector to the area of sphere with direction along the radius and outward.
4.29)
4.30)
4.32)
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