A particle completes 1.5 revolutions in a circular path of radius 2 cm. The angular displacement of the particle will be – (in radian)

The correct option is 3 π.

Step-by-step Explanation:

1. Understand Angular Displacement in One Revolution:
When a particle completes one full revolution (one complete circle) in a circular path, the angle swept or angular displacement is equal to 360 degrees, which in radians is:
$\theta =2\pi \text{radians}$

2. Calculate for 1.5 Revolutions:
The particle completes 1.5 revolutions. To find the total angular displacement ($\theta$), we multiply the number of revolutions by the angular displacement per revolution:
$\theta =1.5\times 2\pi \text{radians}$

3. Simplify the expression:
$\theta =\frac{3}{2}\times 2\pi \text{radians}$
$\theta =3\pi \text{radians}$

Therefore, the angular displacement of the particle is 3 π radians. Note that the radius of the circular path (2 cm) is extra information and is not required to calculate the angular displacement.