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29/12/2021 1:15 pm
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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 revolutions if its speed is 8 Au per second?
(a) 3.5 × 106 S
(b) 4.5 × 106 S
(c) 7.2 × 108 S
(d) 4.1 × 108 S
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29/12/2021 1:21 pm
Correct answer: (b) 4.5 × 106 S
Explanation:
l = 4.4 ly = 4.4 × 9.46 × 1015
Length of Arc = l = R θ
4.4 × 9.46 × 1015 = R θ
θ = 4S = 4 × 4.843 × 10-6 = 1.94 × 10-5 rad
4.4 × 9.46 × 1015 = R × 1.94 × 10-5
4 revolution means distance = 4 × 2 πR meter
Time = \(\frac{distance}{speed}\)
= \(\frac{4 \times 2 \pi R}{12 \times 10^{11}}\)
time = \(\frac{8 \times 3.14 \times 2.1455 \times 10^{21}}{12 \times 10^{11}}\)
⇒ 4.5 × 1010 sec