An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensional formula of constant of proportionality is

Question

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensional formula of constant of proportionality is (A)  [ML-1T-1] (B)  [MLT-1]  (C)  [M0LT-1]  (D)  [ML0T-1]

Tardigrade Admin · Accepted Answer

F propto v ⇒ F=kv ⇒ [k] =[ (F/v) ]=[ (MLT-2/LT-1) ] =[ML0T-1]

Q. An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensional formula of constant of proportionality is

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

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

$[M^{0} L T^{- 1}]$

$[M L^{0} T^{- 1}]$

$F \propto v$
$\Rightarrow F = k v$
$\Rightarrow [k]$
$= [\frac{F}{v}] = [\frac{M L T ^{- 2}}{L T ^{- 1}}]$
$= [M L^{0} T^{- 1}]$

Q. An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensional formula of constant of proportionality is

[ML−1T−1]

[MLT−1]

[M0LT−1]

[ML0T−1]

F∝v ⇒F=kv ⇒[k] =[vF​]=[LT−1MLT−2​] =[ML0T−1]

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

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

$[M^{0} L T^{- 1}]$

$[M L^{0} T^{- 1}]$

$F \propto v$
$\Rightarrow F = k v$
$\Rightarrow [k]$
$= [\frac{F}{v}] = [\frac{M L T ^{- 2}}{L T ^{- 1}}]$
$= [M L^{0} T^{- 1}]$