Question

# A dimensionless quantity :

A

May have a unit

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B

Never has a unit

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C

Always has a unit

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D

Does not exist

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Solution

## The correct option is A May have a unitDimensional analysis covers three parameters namely mass, length and time.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.$Linearstrain=\frac{changeinlength}{originallength}$However, there are certain quantities like “angle” which are dimensionless but still have units.There are no dimensions of an angle but an angle has the units of radians or degrees.Hence, a dimensionless quantity may have units.Hence, option (A) is correct.

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