Question

A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the stataments is incorrect ?

• A. Displacement of the particle is zero.
• B. Average speed of the particle is zero.
• C. Average velocity of the particle is zero.
• D. Average acceleration of the particle is zero.

Answer 1

The Correct Option is B

Given: 

A particle is in uniform circular motion, completing one full revolution.

Step 1: Understanding Key Concepts

• Displacement: The shortest distance between the initial and final positions. Since the particle returns to the same point, displacement is zero.
• Average Speed: Defined as total distance traveled divided by time. The total distance in one revolution is the circumference, which is not zero.
• Average Velocity: Defined as total displacement divided by time. Since displacement is zero, average velocity is also zero.
• Average Acceleration: Uniform circular motion has a centripetal acceleration, but over one complete revolution, the average acceleration vector sums to zero.

Step 2: Identifying the Incorrect Statement

The incorrect statement is:

"Average speed of the particle is zero." (since speed is always positive in motion).

Answer: The correct option is B.

Answer 2

In uniform circular motion, the particle moves along a circular path with a constant speed. Let’s evaluate the given options based on one complete revolution of the particle:

(A) Displacement of the particle is zero.
Displacement is the vector quantity that represents the change in the position of the particle. After one complete revolution, the particle returns to its initial position, so the displacement is indeed zero.

(B) Average speed of the particle is zero.
The average speed is defined as the total distance traveled divided by the total time taken. In one complete revolution, the particle travels a distance equal to the circumference of the circle. Since the particle is moving with a constant speed, the average speed is not zero. Therefore, this statement is incorrect.

(C) Average velocity of the particle is zero.
The average velocity is defined as the displacement divided by the total time. Since the displacement is zero after one complete revolution, the average velocity is zero.

(D) Average acceleration of the particle is zero.
The particle is continuously changing direction during its circular motion, meaning it is accelerating. The average acceleration is not zero because there is a centripetal acceleration directed towards the center of the circle at every point in the motion.

Thus, the incorrect statement is (B).

\(\textbf{Correct Answer:}\) (B) Average speed of the particle is zero.