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.

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Solution

(a) True, because magnitude is a pure number and directionless.
(b) False, vector is sum of its components.(Note: Magnitude of each component is a scalar)
(c) False, because total path length is greater than or equal to magnitude of displacement vector, whenever direction of motion changes.
(d) True, because the total path length is either greater than or equal to the magnitude of the displacement vector.
(e) True, as they can not be represented by the three sides of a triangle taken in the same order.

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Similar questions

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.

Q. State the following statement is True or False:
The total path length is always equal to the magnitude of the displacement vector of a particle.

Explain clearly, with examples, the distinction between:
a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;
b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.
When is the equality sign true? [For simplicity, consider one-dimensional motion only].

Q. Assertion :The average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval Reason: The two are equal only if the path length is equal to the magnitude of displacement.

The magnitude of component of a vector must be

1- less than the magnitude of vector always

2-equal to magnitude of vector always

3- always greater than magnitude of vector

4-None of the above

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