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JEE Main 202127 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Morning Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2021 · 27 August · Morning Shift · Physics · Rotational Motion

A huge circular arc of length 4 . 4ly subtends an angle 4s at the...

A huge circular arc of length 4.4ly4 . 4ly subtends an angle 4s4s at the centre of the circle. How long it would take for a body to complete 44 revolution if its speed is 8AU8AU per second?
Given : 1ly=9.46×1015m1ly = 9 . 46 \times {10}^{15}m

1AU=1.5×1011m1AU = 1 . 5 \times {10}^{11}m

A huge circular arc of length 4 . 4ly subtends an angle 4s at the centre of the circle. How long it would take for a

Options

  1. A3.5×106s3 . 5 \times {10}^{6}s
  2. B4.5×1010s4 . 5 \times {10}^{10}s
  3. C4.1×108s4 . 1 \times {10}^{8}s
  4. D7.2×1087 . 2 \times {10}^{8}

Correct answer

B. 4.5×1010s4 . 5 \times {10}^{10}s

Step-by-step solution

A huge circular arc of length 4 . 4ly subtends an angle 4s at the centre of the circle. How long it would take for a

ℓ=4.4ly=4.4×9.46×1015ℓ = 4 . 4ly = 4 . 4 \times 9 . 46 \times {10}^{15}

length of Arc. =ℓ=Rθ= ℓ = R\theta

4.4×9.46×1015=Rθ4 . 4 \times 9 . 46 \times {10}^{15} = R\theta

θ=4S=4×4.843×10−6=1.94×10−5\theta = 4S = 4 \times 4 . 843 \times {10}^{- 6} = 1 . 94 \times {10}^{- 5} rad

4.4×9.46×1015=R×1.94×10−54 . 4 \times 9 . 46 \times {10}^{15} = R \times 1 . 94 \times {10}^{- 5}

R=2.1455×1021R = 2 . 1455 \times {10}^{21} meter

Speed =8Au=8×1.5×1011ms−1=12×1011ms−1= 8Au = 8 \times 1 . 5 \times {10}^{11}{ms}^{- 1} = 12 \times {10}^{11}{ms}^{- 1}

44 revolution means distance =4×2\piR= 4 \times 2\piR metre

time =distancespeed=4×2\piR12×1011;= \dfrac{\text{distance}}{\text{speed}} = \dfrac{4 \times 2\piR}{12 \times {10}^{11}}; time =8×3.14×2.1455×102112×1011⇒4.5×1010sec= \dfrac{8 \times 3 . 14 \times 2 . 1455 \times {10}^{21}}{12 \times {10}^{11}} ⇒ 4 . 5 \times {10}^{10}sec

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