Question

The angular diameter of the sun is 1920". If the distance of the sun from the earth is $1.5\times {10}^{11}$m, then the linear diameter of the sun is :

• A. $2.6\times {10}^9$ m
• B. $0.7\times {10}^9$ m
• C. $5.2\times {10}^9$ m
• D. $1.4\times {10}^9$ m

Answer 1

Answer: (D)

$1.4\times {10}^9$ m

Angular diameter $\theta ={1920}^{\prime \prime }=\frac{1920}{60}={32}^{\prime }$
We know that $1^{\prime }={\frac{1}{60}}^o=\frac{1}{60}\times \frac{\pi }{180}rad$
$\therefore \theta =32\times \frac{\pi }{60\times 180}=0.009rad$
Distance between sun and earth $l=1.5\times {10}^{11}m$
Linear diameter $d=l\theta =1.5\times {10}^{11}\times 0.009=1.4\times {10}^{9}m$