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In which of the following cases of motions, the distance moved and the magnitude of the displacement are equal?
i. If the car is moving on a straight road
ii. If the car is moving in circular path
iii. The pendulum is moving to and fro
iv. The earth is moving around the sun
- a)only (ii)
- b)(i) and (iii)
- c)(ii) and (iv)
- d)only (i)
Correct answer is option 'D'. Can you explain this answer?
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In which of the following cases of motions, the distance moved and th...
If the car is moving on a straight road than the displacement is always equal to the distance, when an object is moving in the a straight path (displacement is defined as the shortest distance covered by a body)
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In which of the following cases of motions, the distance moved and th...
Explanation:
Motions and Distance vs. Displacement:
Distance is the total length covered by an object in motion regardless of its direction, while displacement is the shortest distance between the initial and final positions along with its direction.
Case (i): Car moving on a straight road
- In this case, if the car moves in a straight line, the distance covered by the car and the displacement of the car are equal because the car moves in a single direction without changing its path.
Therefore, in this case, the distance moved and the magnitude of the displacement are equal.
Case (ii): Car moving in a circular path
- In this case, when a car moves in a circular path, the distance covered by the car is the total length of the circular path, whereas the displacement is the distance measured from the initial position to the final position in a straight line.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Case (iii): Pendulum moving to and fro
- When a pendulum moves back and forth, the distance covered by the pendulum is the total length of the path it swings, and the displacement is the straight-line distance between the initial and final positions.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Case (iv): Earth moving around the sun
- The earth's motion around the sun is in an elliptical orbit, and the distance covered by the earth in one revolution is the circumference of the elliptical path. The displacement of the earth is the straight-line distance between the initial and final positions.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Therefore, the correct answer is option (D) only (i).
Motions and Distance vs. Displacement:
Distance is the total length covered by an object in motion regardless of its direction, while displacement is the shortest distance between the initial and final positions along with its direction.
Case (i): Car moving on a straight road
- In this case, if the car moves in a straight line, the distance covered by the car and the displacement of the car are equal because the car moves in a single direction without changing its path.
Therefore, in this case, the distance moved and the magnitude of the displacement are equal.
Case (ii): Car moving in a circular path
- In this case, when a car moves in a circular path, the distance covered by the car is the total length of the circular path, whereas the displacement is the distance measured from the initial position to the final position in a straight line.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Case (iii): Pendulum moving to and fro
- When a pendulum moves back and forth, the distance covered by the pendulum is the total length of the path it swings, and the displacement is the straight-line distance between the initial and final positions.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Case (iv): Earth moving around the sun
- The earth's motion around the sun is in an elliptical orbit, and the distance covered by the earth in one revolution is the circumference of the elliptical path. The displacement of the earth is the straight-line distance between the initial and final positions.
Therefore, in this case, the distance moved and the magnitude of the displacement are not equal.
Therefore, the correct answer is option (D) only (i).
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In which of the following cases of motions, the distance moved and the magnitude of the displacement are equal? i. If the car is moving on a straight roadii. If the car is moving in circular pathiii. The pendulum is moving to and froiv. The earth is moving around the suna) only (ii)b) (i) and (iii)c) (ii) and (iv)d) only (i)Correct answer is option 'D'. Can you explain this answer?
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