Question

Match the physical quantities given in Column I with their dimensional formula given in ColumnII

Column-I	Column-II
(a) Thermal conductivity	(p) is a dimensionless quantity
(b) Stefans constant	(q) $M{L}^o{T}^{o}K$
(c) Wiens constant	(r) $M{L}^2{T}^{-3}{K}^{-1}$
(d) Emissivity	(s) $M{L}^o{T}^{-3}{K}^{-4}$

• A. a-s, b-r, c-p, d-q
• B. a-r, b-s, c-q, d-p
• C. a-s, b-q, c-r, d-p
• D. a-p, b-q, c-r, d-s

Answer 1

The correct option is B a-r, b-s, c-q, d-p

Thermal resistance $=\frac{kelvin}{watt}$
Unit of power is watt so power = force$\times$ velocity
Force = mass$\times$acceleration = M$\times$$\frac{m}{{sec}^2}$
Force = $ML{T}^{-2}$
Power = $M{L}^2{T}^{-3}$
So, Thermal resistance $=M^{-1}{L}^{-2}{T}^3\theta$
and we know that relation between conductivity and resistevity is that they are reciprocal to each other,so thermal conductivity =$M^1{L}^2{T}^{-3}{\theta }^{-1}$

Stefan's constant $=5.64\times$${10}^{-8}$$\frac{w}{m^2{k}^4}$
$\sigma$=$M{L}^0{T}^{-3}{\theta }^4$

Wein's constant: $\lambda \theta$ = constant = [$L\theta$]

Emissivity is define as the ration of two same quantity so it is dimensionless.