Question

The solar energy on the roof in one hour of dimension $8m \times 20m$ will be :
(A) $5.76 \times {10^8}J$
(B) $5.76 \times {10^7}J$
(C) $5.76 \times {10^6}J$
(D) $5.76 \times {10^5}J$

Answer 1

Hint We know that the intensity of light is the light energy per unit area per unit second. In that formula put the values of the given quantities and calculate the value of the unknown quantity i.e. solar energy.

Complete step-by-step answer Light is a form of energy. Light sensitive devices make use of this light energy. They are sensitive to the power of light, or how much solar( light) energy is arriving per unit time. Intensity is the amount of energy per unit area per unit time. We know the intensity of luminous light and with the help of this formula we will calculate the value of the solar energy.
We know that : $Intensity = \dfrac{{Energy}}{{area \times time}}$
So to calculate the energy of the system we have:
$Energy = Intensity \times area \times time$ ……..(i)
We now need to calculate intensity, area and time individually.
The intensity depends on the number of light (or sun) rays falling on that particular surface at that particular instance.
The intensity of the sun $= 1.0\dfrac{{KW}}{{{m^2}}} = 1 \times 1000\dfrac{W}{{{m^2}}}$
The dimensions are given to us, length and breadth, we will now calculate the area. The roof is rectangular.
Area of the roof $= 8 \times 20 \\\ = 160{m^2} \\\$
The time needs to be converted into seconds.
Time ( in seconds) $= 60 \times 60 \\\ = 3600s \\\$
Putting these values in eq (i), we will have –
We will calculate the energy now that we have the values of intensity, area, and time.
$Energy = 1.0 \times 1000 \times 160 \times 3600 \\\ Energy = 5.76 \times {10^8}J \\\$

We have got the answer. Hence, the correct option is A.

Note- More the intensity of light, more will be the brightness and vice- versa. Light energy travels in the form of photons. Each photon has some energy associated with it, we are calculating that energy only.