(solved)Question 2.32 of NCERT Class XI Physics Chapter 2

Question 2.32
NCERT Class XI Physics

It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.

Solution
[see video for diagram]

Let angle subtended by earth's dia on moon $\displaystyle \theta_1$

Let earth's diameter $\displaystyle b_1$

by parallax formula distance of moon $\displaystyle D_1 = \frac{b_1}{\theta_1}$

Let angle subtended by moon during eclipse $\displaystyle \theta$

by parallax dia of moon $\displaystyle = D_1 \times \theta = \frac{b_1}{\theta_1} \times \theta$

by Ex 2.3 $\displaystyle b_1 = 1.276 \times 10^7 \text{ m, SF = 4}$

by Ex 2.3 $\displaystyle \theta_1 = 114 \times 60\rq\rq$

by Ex 2.4 $\displaystyle \theta = 1920\rq\rq$

Hence dia of moon = $\displaystyle = \frac{1.276 \times 10^7}{114 \times 60} \times 1920$

$\displaystyle = 3.58 \times 10^6 \text{ meters} \:\underline{Ans}$

Video Explanation

Please watch this youtube video for a quick explanation of the solution: