Question:
A huge circular arc of length $4.4$ ly subtends an angle ' $4 s^{\prime}$ at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second ?
Given : $1 \mathrm{lv}=9.46 \times 10^{15} \mathrm{~m}$
$1 \mathrm{AU}=1.5 \times 10^{11} \mathrm{~m}$
Correct Option: , 2
Solution:
$\mathrm{R}=\frac{\ell}{\theta}$
$\operatorname{Time}=\frac{4 \times 2 \pi R}{\mathrm{~V}}=\frac{4 \times 2 \pi}{\mathrm{V}}\left(\frac{\ell}{\theta}\right)$
put $\ell=4.4 \times 9.46 \times 10^{15}$
$\mathrm{v}=8 \times 1.5 \times 10^{11}$
$\theta=\frac{4}{3600} \times \frac{\pi}{180} \mathrm{rad}$
we get time $=4.5 \times 10^{10} \mathrm{sec}$