Question

Match the Column I with Column II.

Column I (Physical quantity)		Column II (Dimensional formula)
(A)	Permittivity of free space	(p)	$[M^0{L}^0{T}^{-1}]$
(B)	Radiant flux	(q)	$[M{L}^3{T}^{-3}{A}^{-2}]$
(C)	Resistivity	(r)	$[M{L}^2{T}^{-3}]$
(D)	Hubble constant	(s)	$[M^{-1}{L}^{-3}{T}^4{A}^2]$

• A. $A-p$, $B-q$, $C-r$, $D-s$
• B. $A-q$, $B-p$, $C-s$, $D-r$
• C. $A-s$, $B-r$, $C-q$, $D-p$
• D. $A-r$, $B-s$, $C-p$, $D-q$

Answer 1

Answer: (C)

Permittivity of free space
$=\frac{\text{Charge × charge}}{4\pi \times {\text{electrical force × distance}}^2}$
$\left[{\epsilon }_0\right]=\frac{\left[AT\right]\left[AT\right]}{\left[ML{T}^{-2}\right]{\left[L\right]}^2}=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
$A-s$
Radiant flux $=\frac{\text{Energy emitted}}{\text{Time}}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[T\right]}=\left[M{L}^2{T}^{-3}\right]$
Resistivity $=\frac{\text{Resistance × Area}}{\text{Length}}$
$\left[\rho \right]=\frac{\left[M{L}^2{T}^{-3}{A}^{-2}\right]\left[L^2\right]}{\left[L\right]}=\left[M{L}^3{T}^{-3}{A}^{-2}\right]$
$C-q$
Hubble constant
$=\frac{\text{Recession speed}}{\text{Distance}}=\frac{\left[L{T}^{-1}\right]}{\left[L\right]}=\left[M^0{L}^0{T}^{-1}\right]$
$D-p$