Correct Answer - Option 2 : Frequency
CONCEPT:
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Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a dimension is a mathematical tool used for studying the nature of physical quantities.
- The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
- And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.
EXPLANATION:
- The is the difference in velocity between the adjacent layers in the fluid and mathematically it is written as
\(\Rightarrow Velocity \,\,gradient=\frac{dV}{dx}\)
- The dimension of velocity gradient is given by
\(\Rightarrow \frac{dV}{dx} = \frac{Dimension \ of \ Velocity}{Dimension \ of \ Distance} = \frac{[LT^{-1}]}{[L]} = [T^{-1}]\)
- The time period is the time taken to complete one cycle of operations so the dimension of the time period is [T].
- Frequency is the number of cycles per second, frequency is measured in Hertz and the dimension is given by
\(\Rightarrow \nu = \frac{1}{Dimension \ of \ time} = \frac{1}{[T]} = [T]^{-1}\)
- The dimension of the velocity gradient is the same as that of frequency. Hence, option 2 is the answer.