Question

The relation between force $F$ and density $d$ is $F=\frac{x}{\sqrt{d}}$. The dimensions of $x$ are

• A. $\left[L^{-1/2}{M}^{3/2}{T}^{-2}\right]$
• B. $\left[L^{-1/2}{M}^{1/2}{T}^{-2}\right]$
• C. $\left[L^{-1}{M}^{3/2}{T}^{-2}\right]$
• D. $\left[L^{-1}{M}^{1/2}{T}^{-2}\right]$

Answer 1

Answer: (A)

$\left[L^{-1/2}{M}^{3/2}{T}^{-2}\right]$

Given, $F=\frac{x}{\sqrt{d}}$
Substituting dimensions
$ML{T}^{-2}=\frac{x}{\sqrt{M{L}^{-3}}}$
$\Rightarrow x=\left[M^{3/2}{L}^{-1/2}{T}^{-2}\right]$