The force F on a sphere of radius r moving in a medium with velocity v given by F=6π η rv . The dimensions of r) are :

Question

The force F on a sphere of radius r moving in a medium with velocity v given by F=6π η rv . The dimensions of r) are : (A)  [ ML-3 ]  (B)  [ MLT2 ]  (C)  [ MT-1 ]  (D)  [ ML-1T-1 ]

Tardigrade Admin · Accepted Answer

Viscous force on a sphere of radius r is F=6π η rv ∴ η =(F/6π rv) |η |=(|F|/|r| |v|)=([MLT-2]/[L][LT-1])=[ML-1T-1] NOTE: The above expression is the Stokes law.

Q. The force F on a sphere of radius r moving in a medium with velocity v given by $F = 6 π ηr v$ . The dimensions of r) are :

$[M L^{- 3}]$

$[M L T^{2}]$

$[M T^{- 1}]$

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

Viscous force on a sphere of radius r is $F = 6 π ηr v$ $∴$ $η = \frac{F}{6 π r v}$ $∣ η ∣ = \frac{∣ F ∣}{∣ r ∣ ∣ v ∣} = \frac{[ M L T ^{- 2} ]}{[ L ] [ L T ^{- 1} ]} = [M L^{- 1} T^{- 1}]$ NOTE: The above expression is the Stokes law.

Q. The force F on a sphere of radius r moving in a medium with velocity v given by F=6πηrv . The dimensions of r) are :

[ML−3]

[MLT2]

[MT−1]

[ML−1T−1]