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

The correct option is A $\left[L^{-1/2}{M}^{3/2}{T}^{-2}\right]$

The dimensions of $x$ are $\left[x\right]=\left[F\right]{\left[d\right]}^{0.5}=\left[ML{T}^{-2}\right]{\left[{ML}^{-3}\right]}^{0.5}=\left[M^{1.5}{L}^{-0.5}{T}^{-2}\right]$