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

Question

An object is moving through the liquid. Tit viscous damping force acting on it a 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. Tit viscous damping force acting on it a 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. Tit viscous damping force acting on it a 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]

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

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

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

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

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