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Question: Answered & Verified by Expert

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=9.46×1015 m

1 AU=1.5×1011 m

PhysicsRotational MotionJEE MainJEE Main 2021 (27 Aug Shift 1)
Options:
  • A 3.5×106 s
  • B 4.5×1010 s
  • C 4.1×108 s
  • D 7.2×108
Solution:
2471 Upvotes Verified Answer
The correct answer is: 4.5×1010 s

=4.4ly=4.4×9.46×1015

length of Arc. ==Rθ

4.4×9.46×1015=Rθ

θ=4 S=4×4.843×10-6=1.94×10-5 rad

4.4×9.46×1015=R×1.94×10-5

R=2.1455×1021 meter

Speed =8Au=8×1.5×1011 ms-1=12×1011 ms-1

4 revolution means distance =4×2πR metre

time = distance  speed =4×2πR12×1011; time =8×3.14×2.1455×102112×10114.5×1010sec

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