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For a particle performing uniform circular motion, choose the incorrect statement form the following.
- a)Magnitude of particle velocity (speed) remains constant.
- b)Particle velocity remains directed perpendicular to radius vector.
- c)Direction of acceleration keeps changing as particle moves.
- d)Magnitude of acceleration does not remain constant.
Correct answer is option 'D'. Can you explain this answer?
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For a particle performing uniform circular motion, choose the incorrec...
For a particle performing uniform circular motion, magnitude of the acceleration remains constant.
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For a particle performing uniform circular motion, choose the incorrec...
Incorrect Statement: The magnitude of acceleration does not remain constant.
Explanation:
Uniform Circular Motion:
Uniform circular motion is a type of motion in which an object moves in a circular path with a constant speed. The object continuously changes its direction but maintains a constant speed throughout the motion.
Velocity in Uniform Circular Motion:
In uniform circular motion, the magnitude of the velocity, also known as the speed, remains constant. This is because the object is moving at a constant speed along the circular path. Therefore, statement (a) is correct.
Direction of Velocity:
The velocity of the object in uniform circular motion is always directed perpendicular to the radius vector of the circular path. This is because the velocity vector is tangential to the circle at any point. Therefore, statement (b) is correct.
Acceleration in Uniform Circular Motion:
Acceleration is the rate of change of velocity. In uniform circular motion, although the speed remains constant, the direction of the velocity vector changes continuously. This means that the velocity vector is always changing, resulting in non-zero acceleration. The acceleration vector is directed towards the center of the circle and is perpendicular to the velocity vector. Therefore, statement (c) is correct.
Magnitude of Acceleration:
The magnitude of acceleration in uniform circular motion is given by the formula a = v²/r, where v is the speed of the object and r is the radius of the circular path. Since the speed remains constant, the magnitude of acceleration does not remain constant. It depends on the radius of the circular path. As the radius changes, the magnitude of acceleration also changes. Therefore, statement (d) is incorrect.
Conclusion:
In uniform circular motion, the correct statement is that the magnitude of acceleration does not remain constant. The other statements, such as the magnitude of particle velocity remains constant, particle velocity remains directed perpendicular to the radius vector, and the direction of acceleration keeps changing as the particle moves, are all correct.
Explanation:
Uniform Circular Motion:
Uniform circular motion is a type of motion in which an object moves in a circular path with a constant speed. The object continuously changes its direction but maintains a constant speed throughout the motion.
Velocity in Uniform Circular Motion:
In uniform circular motion, the magnitude of the velocity, also known as the speed, remains constant. This is because the object is moving at a constant speed along the circular path. Therefore, statement (a) is correct.
Direction of Velocity:
The velocity of the object in uniform circular motion is always directed perpendicular to the radius vector of the circular path. This is because the velocity vector is tangential to the circle at any point. Therefore, statement (b) is correct.
Acceleration in Uniform Circular Motion:
Acceleration is the rate of change of velocity. In uniform circular motion, although the speed remains constant, the direction of the velocity vector changes continuously. This means that the velocity vector is always changing, resulting in non-zero acceleration. The acceleration vector is directed towards the center of the circle and is perpendicular to the velocity vector. Therefore, statement (c) is correct.
Magnitude of Acceleration:
The magnitude of acceleration in uniform circular motion is given by the formula a = v²/r, where v is the speed of the object and r is the radius of the circular path. Since the speed remains constant, the magnitude of acceleration does not remain constant. It depends on the radius of the circular path. As the radius changes, the magnitude of acceleration also changes. Therefore, statement (d) is incorrect.
Conclusion:
In uniform circular motion, the correct statement is that the magnitude of acceleration does not remain constant. The other statements, such as the magnitude of particle velocity remains constant, particle velocity remains directed perpendicular to the radius vector, and the direction of acceleration keeps changing as the particle moves, are all correct.
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For a particle performing uniform circular motion, choose the incorrect statement form the following.a)Magnitude of particle velocity (speed) remains constant.b)Particle velocity remains directed perpendicular to radius vector.c)Direction of acceleration keeps changing as particle moves.d)Magnitude of acceleration does not remain constant.Correct answer is option 'D'. Can you explain this answer?
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