Question

A huge circular arc of length $4.4$ ly subtends an angle '$4s$ ' 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 : $1 ly =9.46 \times 10^{15}m$
$1 AU =1.5 \times 10^{11} m$

• A. $4.1 \times 10^{8} s$
• B. $4.5 \times 10^{10} s$
• C. $3.5 \times 10^{6} s$
• D. $7.2 \times 10^{8} s$

Answer 1

Answer: (B)

$R =\frac{\ell}{\theta}$
Time $=\frac{4 \times 2 \pi R}{ v }=\frac{4 \times 2 \pi}{ v }\left(\frac{\ell}{\theta}\right)$
put $\ell=4.4 \times 9.46 \times 10^{15}$
$v =8 \times 1.5 \times 10^{11}$
$\theta=\frac{4}{3600} \times \frac{\pi}{180} \,rad$
we get time $=4.5 \times 10^{10} \sec$