Question

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

• A. $ML^{- 1}T^{- 1}$
• B. $MLT^{- 1}$
• C. $M^{0}LT^{- 1}$
• D. $ML^{0}T^{- 1}$

Answer 1

Answer: (D)

$ML^{0}T^{- 1}$

Answer 2

$F \propto v \Rightarrow F = kv \Rightarrow \lbrack k\rbrack = \left\lbrack \frac{F}{v} \right\rbrack = \left\lbrack \frac{MLT^{- 2}}{LT^{- 1}} \right\rbrack = \lbrack MT^{- 1}\rbrack$