Question

What is the dimension of Luminous flux?
A. $[c{{d}^{1}}]$
B. $[c{{d}^{1}}{{T}^{-1}}]$
C. $[c{{d}^{1}}{{L}^{-2}}]$
D. $[c{{d}^{1}}{{L}^{1}}{{T}^{-1}}]$

Answer 1

Hint: Convert the mathematical formula of Pressure into basic units in the MKS system. Luminous flux is known as a measure of the perceived power of light. It means the energy of light per unit of time. It's SI unit is the lumen. The dimension of the lumen of [J].

Complete step-by-step answer:
The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.
So luminous flux is defined as a product of luminous intensity and total solid angle.
i.e. luminous flux=luminous intensity×total solid angle
The unit of luminous intensity is candela and denoted as cd.
So the unit of \[luminous\text{ }flux=[cd]\]
Answer is (A)

ADDITIONAL INFORMATION:
Luminous flux is nothing but power per unit time. Its dimension is equal to the dimension of power. Power is nothing but a rate of doing work. Now the question comes how it is equal to power dimension. We know that light emitted by the source used is nothing but luminous flux. And we know that power is nothing but how much light is emitting from source or what is the intensity of the source is nothing but power.
Therefore the dimension of power is given by,
$power=\left[ M{{L}^{2}}{{T}^{-3}} \right]$
So the dimension of \[luminous\text{ }flux=power=\left[ M{{L}^{2}}{{T}^{-3}} \right]\]

Note: Note that luminous flux is not exactly equal to power but we can define it as power. It will not make a big change. Students usually try to memorize the SI units, but it is a wrong way to do these types of questions. Students should only memorize the basic formulas, and they should convert the given formula into basic units to dimensional formula or SI units.