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Question :

Read each statement below carefully and state, with reasons, if it is true or false :
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

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Last updated date: 13th Jun 2024
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Answer
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Hint: You can apply the principles of circular motion, velocity, and acceleration to determine the correctness of these statements.


Step-by-Step Solutions:

(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the center:

Answer: True.

Explanation: This statement is true. In circular motion, the net (centripetal) acceleration is directed radially inward toward the circle's centre. This acceleration is responsible for keeping the particle moving in a circular path. It is always perpendicular to the velocity vector.


(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point:

Answer: True.

Explanation: This statement is true. The velocity vector of a particle at any point in its path is always tangent to the path at that point. It represents the direction of motion at that specific moment, tangential to the circular path.


(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector:

Answer: True.

Explanation: This statement is true. In uniform circular motion (where the speed is constant), the net acceleration averaged over one full cycle is indeed a null vector. This is because the net acceleration is always directed toward the center and is balanced by the centrifugal acceleration (directed outward), resulting in a net acceleration of zero over one complete cycle.


Note:

For statement (a), understanding the concept of centripetal acceleration is crucial in circular motion physics.

For statement (b), the velocity vector is always tangent to the path, indicating the direction of motion.

For statement (c), the uniformity of motion ensures that the net acceleration averages to zero over a full cycle, despite constantly changing direction. This is important in concepts like circular motion and orbits.

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