The force F on a sphere of radius a , moving in a medium with velocity v , is given by F = 6 π η a v . The dimensions of η are

Question

The force F on a sphere of radius a , moving in a medium with velocity v , is given by F = 6 π η a v . The dimensions of η are (A) [ML- 1 T- 1] (B) [MT- 1] (C) [MLT- 2] (D) [ML- 3]

Tardigrade Admin · Accepted Answer

η=(F/a v)=([. MLT- 2 ]./[. L ]. [. LT- 1 ].)=[ML- 1 T- 1]

Q. The force $F$ on a sphere of radius $a$ , moving in a medium with velocity $v$ , is given by $F = 6 π η a v$ . The dimensions of $η$ are

$[M L^{- 1} T^{- 1}]$

$[M T^{- 1}]$

$[M L T^{- 2}]$

$[M L^{- 3}]$

$η = \frac{F}{a v} = \frac{[ M L T ^{- 2} ]}{[ L ] [ L T ^{- 1} ]} = [M L^{- 1} T^{- 1}]$

Q. The force F on a sphere of radius a , moving in a medium with velocity v , is given by F=6πηav . The dimensions of η are

[ML−1T−1]

[MT−1]

[MLT−2]

[ML−3]