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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

The correct dimensions of the coefficient of viscosity η are

The correct dimensions of the coefficient of viscosity ηη are

Options

  1. A[ML−1T−2][ \text{M} L^{-1} T^{- 2} ]
  2. B[MLT−1][ \text{M} \text{L} T^{- 1 } ]
  3. C[ML−1T−1][ \text{M} L^{- 1} T^{- 1} ]
  4. D[ML−2T−2][ \text{M} L^{- 2} T^{- 2} ]

Correct answer

C. [ML−1T−1][ \text{M} L^{- 1} T^{- 1} ]

Step-by-step solution

Viscous force is given as, F=6πηrvF = 6\pi η\text{r}v.

∴η=F6πrv∴ η = \dfrac{F}{6\pi\text{r}v}

[η]=[F][r][v][ η ] = \dfrac{[ F ]}{[ \text{r} ] [ v ]}

[η]=[MLT−2][L][LT−1][ η ] = \dfrac{[ {MLT}^{- 2} ]}{[ \text{L} ] [ {LT}^{- 1} ]}

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