Question

Match the Column I with Column II.

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

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