Question

Physical quantities in Column 1 are represented in the form of dimensional formulae (Column 2) and some derived formulae(Column 3) (where P $\to$ momentum, V $\to$ potential difference, m $\to$ mass, E $\to$ electric field, J $\to$ current density, h $\to$ Planck’s constant , C $\to$ speed of light, $\lambda \to$ wavelength, ${\epsilon }_0\to$ permittivity of vacuum, Q $\to$ charge).
$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ \left(I\right)& LatentHeat& \left(i\right)& M{L}^{-1}{T}^{-2}& \left(P\right)& \frac{P^2}{m{V}^2}\\ \left(II\right)& Capacitance& \left(ii\right)& L^2{T}^{-2}& \left(Q\right)& \frac{E}{J}\\ \left(III\right)& Energydensity& \left(iii\right)& M{L}^3{t}^{-1}{Q}^{-2}& \left(R\right)& {\epsilon }_0{R}^2\\ \left(IV\right)& Resistivity& \left(iv\right)& M^{-1}{L}^{-2}{T}^2{Q}^2& \left(S\right)& \frac{hC}{\lambda m}\end{array}$
Which of the following combination dimensionally matches with $\left(\frac{1}{{\mu }_0{\epsilon }_0}\right)$?

• A. I (ii) Q
• B. I (ii) S
• C. III (i) Q
• D. III (i) R

Answer 1

The correct option is B I (ii) S

$Velocity=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\Rightarrow (velocity{)}^2=\frac{1}{{\mu }_0{\epsilon }_0}=[L^2{T}^{-2}]Also\to Latentheat=[L^2{T}^{-2}]$