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 $8AU$ per second ?
Given : $1ly=9.46\times 10^{15}m$
$1AU=1.5\times 10^{11}m$

• 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 $=4.5\times 10^{10}\sec$