### Question 2.24

NCERT Class XI Physics

When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.

### Solution in Brief

(detailed solution given after the video below)

Parallax angle is small so parallax formula b = D θ is applicable. Substituting, b = (824.7 x 10^6 km) x 35.72" and using 1" = 4.85 x 10^-6 radians, we get b = 1.429 x 10^8 meters (Answer).

### Video Explanation

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

### Solution in Detail

$ \begin{aligned} &\text{Given, }\\ &\text{(i) parallax angle } \theta = 35.72\rq\rq\\ &\text{(ii) distance } D = 824.7 \times 10^6 \text{ km}\\ &\text{SF in D} =4 \text{, and SF in } \theta = 4\\\\ &\text{by parallax equation } b = D \times \theta\\\\ &\therefore b = 824.7 \times 10^6 \text{ km} \times 35.72\rq\rq\\\\ &\text{but } 1\rq\rq = 4.85 \times 10^{-6} \text{ rad}\\ &\text{and } 1\text{ km} = 1000 \text{ m}\\\\ &\therefore b = 824.7 \times 10^9 \times 35.72 \times 4.85 \times 10^{-6}\\ &b = 1.42872 \times 10^8 \text{ m}\\\\ &\text{due to multiplication, SF in } b \\ &\text{will be min(D, } \theta \text{), i.e., } 4\\\\ &\text{rounding, } b = 1.429 \times 10^8 \text{ m} \:\underline{Ans} \end{aligned} $

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