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Dimensions of velocity gradient are same as that of:
1. Time period
2. Frequency
3. Angular acceleration
4. Acceleration

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Correct Answer - Option 2 : Frequency

CONCEPT:

  • 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 masslength, 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.

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