Motion in a Plane
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Question : 5
Total: 32
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) 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.
Solution:
(a) True; because magnitude of a vector is a pure number.
(b) False; as each component of a given vector is always a vector.
(c) True; only if the particle moves along a straight line in the same direction otherwise false.
(d) True; because the totalpath length is either greater than or equal to the magnitude of the displacement vector, so the average speed is greater or equal to the magnitude of average velocity.
(e) True; as they cannot be represented by the three sides of a triangle taken in thesame order. Here the resultant of any two vectors will be in the plane of these two vectors only and it cannot balance the third vector which is in a different plane. Two vectors can cancel each other’s effect only if they are equal in magnitude and oppositein direction.
(b) False; as each component of a given vector is always a vector.
(c) True; only if the particle moves along a straight line in the same direction otherwise false.
(d) True; because the totalpath length is either greater than or equal to the magnitude of the displacement vector, so the average speed is greater or equal to the magnitude of average velocity.
(e) True; as they cannot be represented by the three sides of a triangle taken in thesame order. Here the resultant of any two vectors will be in the plane of these two vectors only and it cannot balance the third vector which is in a different plane. Two vectors can cancel each other’s effect only if they are equal in magnitude and oppositein direction.
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