Question

A particle completes 2 revolutions in a circular path of radius 3 cm. The angular displacement of the particle will be (in radian)

• A. \(π\)
• B. \(2π\)
• C. \(3π\)
• D. \(4π\)

Hint:

One revolution is 2 pi radians; the radius does not matter.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Angular displacement is the angle swept by the radius line. One full revolution sweeps an angle of \(2\pi\) radians, whatever the radius.

Step 2: Calculation
\[ \theta=2\ \text{revolutions}\times2\pi\ \frac{\text{rad}}{\text{rev}}=4\pi\ \text{rad} \]

Step 3: Why the radius is not used
The radius of 3 cm would matter only for the distance travelled, which is \(s=r\theta=3\times4\pi=12\pi\) cm. The question asks for the angle, which depends only on the number of turns.

Step 4: Check the options
\(\pi\) is half a turn, \(2\pi\) is one turn and \(3\pi\) is one and a half turns. Two full turns give \(4\pi\), option (D).

Final Answer:
Two revolutions sweep 4 pi radians, option (D). \[ \boxed{4\pi} \]