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Question: The force \(F\) on a sphere of radius \('a'\) moving in a medium with velocity \('v'\) is given by \...

The force FF on a sphere of radius ′a′'a' moving in a medium with velocity ′v′'v' is given by F=6πηavF = 6\pi\eta av. The dimensions of η\eta are

A

ML−1T−1ML^{- 1}T^{- 1}

B

MT−1MT^{- 1}

C

MLT−2MLT^{- 2}

D

ML−3ML^{- 3}

Answer

ML−1T−1ML^{- 1}T^{- 1}

Explanation

Solution

η=Fav=[MLT−2][L][LT−1]=[ML−1T−1]\eta = \frac{F}{av} = \frac{\lbrack MLT^{- 2}\rbrack}{\lbrack L\rbrack\lbrack LT^{- 1}\rbrack} = \lbrack ML^{- 1}T^{- 1}\rbrack