Question

A dimensionless quantity :

• A. May have a unit
• B. Never has a unit
• C. Always has a unit
• D. Does not exist

Answer 1

The correct option is A

May have a unit

1. Dimensional analysis covers three parameters namely mass, length and time.
2. Linear strain is the ratio of the change in length and the final length of a body and since it is the ratio of two similar quantities, therefore the dimensions in the numerator and the denominator cancel each other making it unit-less and dimensionless.
3. $Linearstrain=\frac{changeinlength}{originallength}$
4. However, there are certain quantities like “angle” which are dimensionless but still have units.
5. There are no dimensions of an angle but an angle has the units of radians or degrees.
6. Hence, a dimensionless quantity may have units.

Hence, option (A) is correct.