JEE MAIN - Physics (2021 - 27th August Morning Shift - No. 7)
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 $$\times$$ 1015 m
1 AU = 1.5 $$\times$$ 1011 m
Given : 1 ly = 9.46 $$\times$$ 1015 m
1 AU = 1.5 $$\times$$ 1011 m
4.1 $$\times$$ 108 s
4.5 $$\times$$ 1010 s
3.5 $$\times$$ 106 s
7.2 $$\times$$ 108 s
Explanation
$$R = {l \over \theta }$$
Time $$ = {{4 \times 2\pi R} \over v} = {{4 \times 2\pi } \over v}\left( {{l \over \theta }} \right)$$
put l = 4.4 $$\times$$ 9.46 $$\times$$ 1015
v = 8 $$\times$$ 1.5 $$\times$$ 1011
$$\theta = {4 \over {3600}} \times {\pi \over {180}}$$ rad.
we get time = 4.5 $$\times$$ 1010 sec.
Time $$ = {{4 \times 2\pi R} \over v} = {{4 \times 2\pi } \over v}\left( {{l \over \theta }} \right)$$
put l = 4.4 $$\times$$ 9.46 $$\times$$ 1015
v = 8 $$\times$$ 1.5 $$\times$$ 1011
$$\theta = {4 \over {3600}} \times {\pi \over {180}}$$ rad.
we get time = 4.5 $$\times$$ 1010 sec.
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