Units & Dimensions

JEE Main level, single correct, medium

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Question 2 of 149

A new unit (α)(\alpha) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of α\alpha units if light takes 66 min. 4040 s to cover this distance?

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Answer: (B) 400 α400\,\alpha

Given that the new unit of length α\alpha is chosen such that the speed of light in vacuum is 1 α/s1\,\alpha/\text{s}.

Time taken by light to cover the distance, t=6 min 40 st = 6\text{ min } 40\text{ s}

t=6×60 s+40 s=400 st = 6 \times 60\text{ s} + 40\text{ s} = 400\text{ s}

Distance between Venus and Earth is given by d=c×td = c \times t

d=1 α/s×400 s=400 αd = 1\,\alpha/\text{s} \times 400\text{ s} = 400\,\alpha

Answer: 400 α400\,\alpha

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