The sun's 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 then?

Sun’s diameter (d) = ${1.494\times {{10}^{11}}m}$

Sun’s angular diameter ($\alpha$) = $1920''$

$1''=4.85\times {{10}^{-6}}rad$

⸫ $1920''$= $1920\times 4.85\times {{10}^{-6}}=9.31\times {{10}^{-3}}rad$= $\alpha$

Sun’s diameter (D) = $\alpha \times d$

D = ($9.31\times {{10}^{-3}}\times 1.494\times {{10}^{11}}$)m

⸫ D = $1.39\times {{10}^{9}}m$

Hence, the correct option is (a) $1.39\times {{10}^{9}}m$