Motion in a Plane
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4.10 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.
4.10 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.
4.10
Since the motorist taking the 60° turn after every 500m, It will form a perfect hexagon of side 500m after 6 turns.
Suppose the motorist starts from point A. From A, turns 60° to reach B (first turn), then to C and so on.
1. At third turn, The magnitude of displacement = DG
Upvote 
4.9 A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the
(a) Net displacement
(b) Average velocity
(c) Average speed of the cyclist?
4.9 A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the
(a) Net displacement
(b) Average velocity
(c) Average speed of the cyclist?
4.9
(a) Since the cyclist came back to his starting point O, so the displacement is Zero
(b) Average velocity = = 0
(c) Average speed =
Distance travelled = OP + PQ + QO
= 1 + (1/4) 3.57 km
Average speed = 3.57 / 10 km/min = 21.43 km/h
Upvote 4.8 Three girls skating on a circular ice ground of radius 200 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?
4.8 Three girls skating on a circular ice ground of radius 200 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?
4.8 The radius of the ground = 200 m, the distance PQ = diameter of the ground = 400 m
The displacement all 3 girls = 400 m
This magnitude is equal to the path skated by girl B
Upvote 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?
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?
4.7
(a) This statement is In order to make a + b+ c + d = 0, it is not necessary to have all four given vectors to be null vectors.
(b) a + b + c +d = 0, ( a + c ) = - (b + d)
Taking the magnitude of both LHS and RHS, | a + c| = | -(b + d)| = | b + d|
So the statement is True.
(c) Given a + b + c +
Upvote 4.6 Establish the following vector inequalities geometrically or otherwise:
(a) |a+b| < |a| + |b|
(b) |a+b| > a| −|b
(c) |a−−b| < |a| + |b|
(d) |a−−b| > a| − |b
When does the equality sign above apply?
4.6 Establish the following vector inequalities geometrically or otherwise:
(a) |a+b| < |a| + |b|
(b) |a+b| > a| −|b
(c) |a−−b| < |a| + |b|
(d) |a−−b| > a| − |b
When does the equality sign above apply?
(a)
We can write
=
= = ………(ii)
=
In a triangle, each side is smaller than the sum of the other two sides. Therefore in ΔOMN, we have ON < (OM + MN)
< + ….(iv)
If the two vectors and act along a straight line in
Upvote 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
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
4.5
(a) The magnitude of a vector is a number only, hence always a scalar – TRUE
(b) Each component of a vector is also a vector – FALSE
(c) The total path length is a scalar quantity, whereas displacement is a vector quantity. – FALSE
(d) The total path length is always greater than or equal to th
Upvote 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
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
4.4
(a) The addition of two scalar quantities is meaningful – if they both represent the same physical quantity.
(b) The addition of a vector quantity with a scalar quantity is not meaningful.
(c) Multiplying a scalar with a vector is meaningful.
(d) The multiplication of two scalar quantities is m
Upvote 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.
4.3 Pick out the only vector quantity in the following list: Temperature, pressure, impulse, time, power, total path length, energy
4.3 Impulse is the only vector quantity from the above list. Impulse is the product of force and time. Force is a vector quantity and time is a scalar quantity. The product of 1 vector and 1 scalar is always a vector quantity.
Upvote 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.
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.
4.2 Work & Current are scalar quantities. Work is the product of Force and displacement. Since the product of two vectors quantities are always scalar. Current is independent of direction, it is only magnitude, hence scalar.
Upvote 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.
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.
4.1 A scalar quantity depends only on the magnitude – volume, mass, speeds, density, number of moles, angular frequency are all scalar quantities.
A vector quantity depends on magnitude and direction – velocity, acceleration, displacement and angular velocity are all vector quantities.
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