Question

The suns angular diameter is measured to be $1920$". The distance of the sun from the earth is $1.496 \times 10^{11}\, m$. What is the diameter of the sun ?

• A. $1.39 \times 10^9\,m$
• B. $1.39 \times 10^{10}\,m$
• C. $1.39 \times 10^{11}\,m$
• D. $1.39 \times 10^{12}\,m$

Answer 1

Answer: (A)

Here,
Distance of the sun from the earth, $d = 1.496 \times 10^{11}\, m$
Suns angular diameter, $\alpha = 192''$
$\because 1''=4.85 \times 10^{-6}\,rad$
$\therefore \alpha = 1920 \times 4.85 \times 10^{-6}\,rad$
$=9.31 \times 10^{-6}\,rad$
Suns diameter, $D = \alpha d$
$D=\left(9.31 \times 10^{-3}\right)\left(1.496 \times 10^{11}\right)m$
$=1.39 \times10^{9}\,m$