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Units And Measurement

Question
CBSEENPH11020461

Which one of the following represents the correct dimensions of the coefficient of viscosity?

  • ML−1 T−2

  • MLT−1

  • ML−1 T−1

  • ML−2 T−2

Solution

C.

ML−1 T−1

straight eta space equals space fraction numerator straight F over denominator straight A left parenthesis increment straight V subscript straight x divided by increment straight z right parenthesis end fraction
therefore space Dimensions space of space straight eta
space equals space fraction numerator Dimensions space of space force over denominator Dimensions space of space area space straight x space Dimensions space of space velocity space gradient end fraction
space equals space fraction numerator left square bracket MLT to the power of negative 2 end exponent right square bracket over denominator left square bracket straight L squared right square bracket left square bracket straight T to the power of negative 1 end exponent right square bracket end fraction space equals space left square bracket ML to the power of negative 1 end exponent straight T to the power of negative 1 end exponent right square bracket