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Which of the following statements false?
- a)the total path length is always equal to the magnitude of the displacement vector of a particle
- b)the magnitude of a vector is always a scalar
- c)three vectors not lying in a plane can never add up to give a null vector.
- 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,
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following statements false?a)the total path length is alw...
Explanation:A displacement is vector that is the shortest path length from the initial to the final position of the body. It is not always eqaul to path length. It can be zero and -ve also.
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Which of the following statements false?a)the total path length is alw...
False Statement:
The false statement is option A: the total path length is always equal to the magnitude of the displacement vector of a particle.
Explanation:
To understand why option A is false, let's first define the terms involved:
1. Path Length: The total distance covered by a particle along its path.
2. Displacement Vector: The change in position of a particle, represented by a vector that has both magnitude and direction.
Now, let's discuss why the total path length is not always equal to the magnitude of the displacement vector of a particle:
1. Scenario 1: Straight Line Motion with No Change in Direction:
- If a particle moves along a straight line without changing its direction, then the path length and displacement vector will have the same magnitude.
- For example, if a particle moves 5 meters to the right, the path length and displacement vector will both have a magnitude of 5 meters.
2. Scenario 2: Curved Motion or Changing Direction:
- If a particle moves along a curved path or changes its direction, the path length will always be greater than or equal to the magnitude of the displacement vector.
- This is because the path length takes into account the total distance covered by the particle, regardless of the direction.
- On the other hand, the displacement vector only considers the change in position, which is the shortest distance between the initial and final positions of the particle.
- For example, if a particle moves in a circle of radius 5 meters, returning to its initial position, the path length will be the circumference of the circle (2π × 5 meters), while the displacement vector will have a magnitude of 0 meters.
Therefore, it is clear that the total path length is not always equal to the magnitude of the displacement vector of a particle.
The false statement is option A: the total path length is always equal to the magnitude of the displacement vector of a particle.
Explanation:
To understand why option A is false, let's first define the terms involved:
1. Path Length: The total distance covered by a particle along its path.
2. Displacement Vector: The change in position of a particle, represented by a vector that has both magnitude and direction.
Now, let's discuss why the total path length is not always equal to the magnitude of the displacement vector of a particle:
1. Scenario 1: Straight Line Motion with No Change in Direction:
- If a particle moves along a straight line without changing its direction, then the path length and displacement vector will have the same magnitude.
- For example, if a particle moves 5 meters to the right, the path length and displacement vector will both have a magnitude of 5 meters.
2. Scenario 2: Curved Motion or Changing Direction:
- If a particle moves along a curved path or changes its direction, the path length will always be greater than or equal to the magnitude of the displacement vector.
- This is because the path length takes into account the total distance covered by the particle, regardless of the direction.
- On the other hand, the displacement vector only considers the change in position, which is the shortest distance between the initial and final positions of the particle.
- For example, if a particle moves in a circle of radius 5 meters, returning to its initial position, the path length will be the circumference of the circle (2π × 5 meters), while the displacement vector will have a magnitude of 0 meters.
Therefore, it is clear that the total path length is not always equal to the magnitude of the displacement vector of a particle.
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Community Answer
Which of the following statements false?a)the total path length is alw...
Condition a can be true only in straight line of motion not in all condition
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Which of the following statements false?a)the total path length is always equal to the magnitude of the displacement vector of a particleb)the magnitude of a vector is always a scalarc)three vectors not lying in a plane can never add up to give a null vector.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,Correct answer is option 'A'. Can you explain this answer?
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