Question

What is the dimension for solar constant?

Answer 1

Hint: As the solar constant is the measurement of the total radiation from the sun per unit of time per unit of area. Therefore its unit is Watt per square meter. After this we will write Watt as joule meter$\left[ {JM} \right]$. Then we will write the units for each variable in terms of Mass, Length, and Time and obtain the final unit for solar constant.

Complete Step-by-Step solution:
 Let us assume M= Mass
                            L= length
                            T=Time
The solar constant is the measurement of the total radiation from the sun per unit of time per unit of area. The estimated value of the solar constant is around 1.36 kilowatts per square meter. Therefore its unit is Watt per square meter.
From here ${\text{Solar Constant = Watt/Mete}}{{\text{r}}^2}$-------------------------------- (1)
And, we also know ${\text{Watt = Joule/Second}}$-------------------------------- (2)
Where ${\text{Joule = Mass} \times Acceleration \times Length}$------------------------------ (3)
And ${\text{Acceleration = Length/tim}}{{\text{e}}^{\text{2}}}$---------------------------------- (4)
So now we will write the formulas in terms of basic units that is length, Mass, and Time

From equation (4) we can write \[{\text{Acceleration}} = \left[ {L/{T^2}} \right] = \left[ {L{T^{ - 2}}} \right]\]--------------- (5)
Substituting equation (5) in equation (3) we will get \[{\text{Joule}} = \left[ {M{L^2}{T^{ - 2}}} \right]\]------------- (6)
Substituting equation (6) in equation (2) we will get ${\text{Watt}} = \left[ {M{L^2}{T^{ - 3}}} \right]$--- (7)
Finally substituting equation (7) in (1) we will get
${\text{Impulse}} = \left[ {M{L^2}{T^{ - 3}}/{L^2}} \right] = \left[ {{M^1}{T^{ - 3}}} \right]$

Therefore the dimensional for Impulse is $\left[ {{M^1}{L^0}{T^{ - 3}}} \right]$.

Note: For these types of questions always try to write the given in terms of its formula then break the formula into smaller basic formulas till we get the most basic formula. Then starting from the most basic formula write its units and go on substitution the obtained unit in larger formula till you obtain the required unit.