Angular Variables question from JEE Main 2021 (27 Aug, Shift 1)

Answer: (b)

1. $\theta = 4'' = \frac{4}{3600} \times \frac{\pi}{180} \approx 1.94 \times 10^{-5}$ rad.
2. $r = \frac{s}{\theta} = \frac{4.4 \times 9.46 \times 10^{15}}{1.94 \times 10^{-5}} \approx 2.15 \times 10^{21}$ m.
3. Distance for 4 revolutions $= 4 \times 2\pi r \approx 5.4 \times 10^{22}$ m.
4. Speed $= 8 \times 1.5 \times 10^{11} = 1.2 \times 10^{12}$ m/s, so $t = \frac{5.4 \times 10^{22}}{1.2 \times 10^{12}} \approx 4.5 \times 10^{10}$ s.
5. So the answer is (b) $4.5 \times 10^{10}$ s.