Question

The dimensions of physical quantity $X$ in the equation Force $=\frac{X}{Density}$ is given by

• A. $\left[M^1{L}^4{T}^{-2}\right]$
• B. $\left[M^2{L}^{-2}{T}^{-1}\right]$
• C. $\left[M^2{L}^{-2}{T}^{-2}\right]$
• D. $\left[M^1{L}^{-2}{T}^{-1}\right]$

Answer 1

Answer: (C)

$\left[X\right]=\left[F\right]\times \left[\rho \right]$
$=\left[ML{T}^{-2}\right]\times \left[\frac{M}{L^3}\right]$
$=\left[M^2{L}^{-2}{T}^{-2}\right]$