Question

A particle is performing U.C.M. along a circle of radius \(R\). In half the period of revolution, its displacement and distance covered are respectively

• A. \(\sqrt{2}R,2πR\)
• B. \(2R,πR\)
• C. \(2R,2πR\)
• D. \(R,πR\)

Hint:

Displacement is the straight line from start to end, and distance is the arc length travelled.

Answer 1

The Correct Option is B

Step 1: Understand the concept
Displacement is the shortest straight line from the starting point to the end point. Distance is the actual length of the path travelled.

Step 2: Half a period
In half the period the particle completes half of the circle, ending at the point diametrically opposite to its start.

Step 3: Displacement
The straight line joining two opposite points of a circle is its diameter, so the displacement is \(2R\).

Step 4: Distance
The path is a half circle, so the distance is half the circumference: \(\frac{1}{2}\times2\pi R = \pi R\). So the answer is displacement \(2R\) and distance \(\pi R\), option (B). The value \(2\pi R\) is the distance for a full revolution, where the displacement would be zero.

Final Answer:
Displacement is 2R and distance is pi R. This is option (B). \[ \boxed{\text{(B) }2R,\ \pi R} \]