Ncert Exercises & Solutions

29. During a total solar eclipse-the moon almost entirely covers the sphere of the sun. The relation between the distances and sizes of the sun and moon is:

$(1) \frac{R_{s}}{R_{m}} = \frac{R_{se}}{R_{me}}$
$(2) \frac{R_{s}}{R_{m}} = {(\frac{R_{se}}{R_{me}})}^{2}$
$(3) \frac{R_{s}}{R_{m}} = \sqrt{\frac{R_{se}}{R_{me}}}$
$(4) \frac{R_{m}}{R_{s}} = \frac{R_{se}}{R_{me}}$

This objective question is based on NCERT Exemplar subjective Question.

Hint: Use the parallax method.

Consider the diagram given below.
$R_{me}$ = distance of the moon from earth
$R_{se}$ = Distance of sun from the earth

Step 1: Find the angles subtended by the sun and the moon.

Let the angle made by the sun and moon is $θ$ , we can write,

$θ = \frac{A_{sun}}{R_{se}^{2}} = \frac{A_{moon}}{R_{me}^{2}}$
$\begin{array}{l} Here, A_{sun} = Area of the sun \\ A_{moon} = Area of the moon \\ Step 2 : Find the relation between R_{se} and R_{me} . \end{array}$
$\begin{array}{l} \Rightarrow θ = \frac{{πR}_{s}^{2}}{R_{se}^{2}} = \frac{{πR}_{m}^{2}}{R_{me}^{2}} \\ \Rightarrow {(\frac{R_{s}}{R_{se}})}^{2} = {(\frac{R_{m}}{R_{me}})}^{2} \\ \Rightarrow \frac{R_{s}}{R_{se}} = \frac{R_{m}}{R_{me}} \\ \Rightarrow \frac{R_{s}}{R_{m}} = \frac{R_{se}}{R_{me}} \end{array}$

(Here, the radius of the sun and moon represents their sizes respectively)

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