Question

The dimension of the physical quantity $x$ in the equation, $F=\frac{x}{\rho }$, where $F$ is force and $\rho$ is 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

The correct option is C $\left[M^2{L}^{-2}{T}^{-2}\right]$

Given,
$F=\frac{x}{\rho }$
$\Rightarrow x=F\rho$
$\Rightarrow \left[x\right]=\left[F\rho \right]$
Dimension of $F=\left[ML{T}^{-2}\right]$
Dimension of $\rho =\left[M{L}^{-3}{T}^0\right]$
$\Rightarrow \left[x\right]=[ML{T}^{-2}\times M{L}^{-3}{T}^0]$
​​​​​​​​​​​​​​$\Rightarrow \left[x\right]=\left[M^2{L}^{-2}{T}^{-2}\right]$