Question

The Solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is
(a) $\left[M^o{L}^o{T}^o\right]$
(b) $[ML{T}^T]$
(c) $[M{L}^2{T}^2]$
(d) $[M{L}^o{T}^3]$

Answer 1

Hint:Use Dimensional Analysis. It is the study of the relationship between the physical quantities with the help of dimensions and the units of measurement. The base quantities here used are mass, length and time.

Complete step by step answer:
 Solar content is defined as energy incident per unit area per second
$S={\displaystyle \frac{Energy}{Area\times Time}}$ ……………(i)
Dimensional Formula for energy is
$=[M^1{L}^2{T}^{-2}]$
Dimensional Formula for Area is
$=[M^o{L}^2{T}^o]$
Dimensional Formula for Time is
$=[M^o{L}^o{T}^1]$
Use these dimensional formula in Equation (i)
$S={\displaystyle \frac{[M^1{L}^2{T}^{-2}]}{[M^o{L}^2{T}^o][M^o{L}^o{T}^1]}}$ ……………(ii)
$=\left[M^1{L}^{2-2}{T}^{-2-1}\right]$
$S=[M^1{L}^o{T}^{-3}]$ ……………(iii)
Hence, Equation (iii) gives the dimensional formula for solar constant.
The correct option is (D): $[M^1{L}^o{T}^{-3}]$

Note: In dimensional formula of any physical quantity. M, L and T are fundamental unit values of quantities. And it is also helpful in identifying the units of physical quantity like in the S.I system. Units of solar Constant is $Kg/s^3.$