11 grade physics others
Give an example of dimensionless quantity but have a unit.
Give an example of dimensionless quantity but have a unit.
1 Answer
Askiitians Tutor Team
Example of a Dimensionless Quantity with a Unit:
Plane angle is a dimensionless quantity but has a unit.
Explanation:
1. Plane Angle as a Dimensionless Quantity:
o A plane angle is defined as the ratio of the length of the arc of a circle (ll) to the radius of the circle (rr): Plane Angle=lr\text{Plane Angle} = \frac{l}{r}
o Since it is a ratio of two quantities with the same physical dimension (length), it is dimensionless.
2. Unit of Plane Angle:
o Although dimensionless, the plane angle is assigned a unit, the radian (rad).
o The unit helps standardize and communicate measurements in practical applications (e.g., in physics, engineering, and mathematics).
Key Takeaway:
A plane angle is dimensionless but is measured in units of radian (rad) to represent its value clearly.
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