The distance of the Sun from earth is $1.5 \times 10^{11} \mathrm{~m}$ and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

(C) $1.45 \times 10^{9} \mathrm{~m}$

(A) $2.45 \times 10^{10} \mathrm{~m}$

(B) $1.45 \times 10^{10} \mathrm{~m}$

(D) $0.14 \times 10^{9} \mathrm{~m}$

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Units & Measurement

The distance of the Sun from earth is

1.5 \times 1 0^{11} m

and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

Answer: (C)

The angular diameter

θ

in radians is related to the actual diameter

d

and distance

r

θ = \frac{d}{r}

. Converting 2000 seconds to radians:

θ = \frac{2000}{3600} \times \frac{π}{180} = \frac{2000 π}{648000}

radians. Then

d = θ \times r = \frac{2000 π}{648000} \times 1.5 \times 1 0^{11} \approx 1.45 \times 1 0^{9}

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option