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: Place the particle
Let the particle start at $(R, 0)$ on a circle centred at the origin. After half a period it is at $(-R, 0)$.

Step 2: Displacement
The vector from $(R, 0)$ to $(-R, 0)$ has length $2R$.

Step 3: Distance
Angle covered is $\pi$ radians, so arc length is $R\theta = \pi R$.

Step 4: Answer
$2R$ and $\pi R$. The option with $\sqrt{2}R$ would be the displacement for a quarter turn, and $R$ would be for a $60^\circ$ turn.

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