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

Answer 1

Answer: (D)

$F\propto v$
$\Rightarrow F=kv$
$\Rightarrow [k]$
$ =\left[ \frac{F}{v} \right]=\left[ \frac{MLT^{-2}}{LT^{-1}} \right]$
$=[ML^{0}T^{-1}]$