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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.
SourceOGQR 2020
TypeData Sufficiency
TopicGeometry/Word Problems
Sub-TopicCircle/Distance
DifficultyMedium

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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