# P is a particle on the circle shown above. What is the length of the path travelled by P in one complete revolution around the circle? – OGQR 2020 Question #212 with Solution

## OGQR 2020: Question No. 212

P is a particle on the circle shown above. What is the length of the path traveled by P in one complete revolution around the circle?

1. The diameter of the circle is 1.5 meters.
2. The particle P moves in a clockwise direction at 0.5 meter per second.

## Solution

### Steps 1 & 2: Understand Question and Draw Inferences

We are given:

• P is a particle on the circle, as shown in the given diagram.

We need to find the length of the path travelled by P in one complete revolution around the circle.

• In one complete revolution, P will cover the entire length of the circle.
• For any circle, its entire length is equal to the perimeter of the circle which is equal to 2πr.
• Thus, we need to find r to find the length of the path travelled by P in one complete revolution around the circle.

With this understanding, let us analyse the statements.

### Step 3: Analyse Statement 1

“The diameter of the circle is 1.5 meters.”

• Diameter = 2 × radius

Hence, we can find the radius from this statement.

Thus, statement 1 is sufficient to answer the question.

### Step 4: Analyse Statement 2

“The particle P moves in a clockwise direction at 0.5 meter per second.”

We know that Distance covered = time × speed

• Here, Speed = 0.5 m/s.
• However, we do not know in how much time P can complete one revolution of the circle.

Hence, we cannot find the length of the path traveled by P in one complete revolution around the circle.

Thus, statement 2 is not sufficient to answer the question.

### Step 5: Combine Both Statements Together (If Needed)

Since we could determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer is option A.

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