A circular arc of length 4.4 light-years subtends an angle 4 s (radian measure) at the centre. How long would a body moving at 8 AU/s take to complete 4 revolutions? (1 ly=9.46×10¹⁵ m, 1 AU=1.5×10¹¹ m)
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Question

A circular arc of length 4.4 light-years subtends an angle 4 s (radian measure) at the centre. How long would a body moving at 8 AU/s take to complete 4 revolutions? (1 ly=9.46×10¹⁵ m, 1 AU=1.5×10¹¹ m)

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G1 Physics · Accepted Answer

The radius is R=s/θ=(4.4 ly)/4=1.1 ly. Four revolutions cover 8πR. Dividing by 8 AU/s and converting ly to metres and AU to metres gives approximately 4.5×10¹⁰ s. Hence B.