Question

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

• A. $ML ^{2} T ^{-2}$
• B. $MLT ^{-2}$
• C. $M ^{2} L ^{0} T ^{-1}$
• D. $ML ^{0} T ^{-3}$

Answer 1

The Correct Option is D

The question asks about the dimensions of the solar constant, defined as the amount of solar energy received on the Earth’s surface per unit area per unit time. Let's break down what this implies in terms of dimensions:

1. Solar constant is essentially a measure of energy per unit area per unit time. Energy, in physics, is often expressed in terms of its dimension: [E] = ML^2T^{-2}, where:
   • M stands for mass
   • L stands for length
   • T stands for time
2. Since the solar constant is energy per unit area, we divide by area which has dimension [A] = L^2. This gives: [Energy/Area] = \frac{ML^2T^{-2}}{L^2} = MT^{-2}
3. Further, as the solar constant measures this energy per unit time, we need to divide by another time dimension: [Energy/Area/Time] = \frac{MT^{-2}}{T} = MT^{-3}

Thus, the dimension of the solar constant is ML^{0}T^{-3}, which matches the given option.

Now, let's evaluate other options to understand why they are incorrect:

• ML^{2}T^{-2}: This is the dimension of energy, not energy flux or intensity.
• MLT^{-2}: This dimension is of force, not relevant to energy per unit area per unit time.
• M^{2}L^{0}T^{-1}: This dimension doesn't correspond to any physical quantity related to energy flux.

Therefore, the correct dimension for the solar constant is ML^{0}T^{-3}.