Question

The damping force $\left(F\right)$ on an object moving with velocity $\left(v\right)$ in a viscous medium is given by $F=k{v}^2$ . The dimensional formula of $k$ is

• A. $\left[M{T}^{-2}\right]$
• B. $\left[M{T}^{-1}\right]$
• C. $\left[M{L}^{-2}\right]$
• D. $\left[M{L}^{-1}\right]$

Answer 1

The correct option is D $\left[M{L}^{-1}\right]$

The damping force acting on objectis given by:

$F=k{v}^2$

$\left[k\right]=\left[\frac{F}{v^2}\right]$

$=\left[\frac{ML{T}^{-2}}{L^2{T}^{-2}}\right]=\left[M{L}^{-1}\right]$