Basic Maths and Units and DimensionsMedium
Question
A new unit ( $\alpha$ ) 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 $\alpha$ units if light takes 6 min. 40 s to cover this distance?
Options
A.$200\alpha$
B.$400\alpha$
C.$300\alpha$
D.$500\alpha$
Solution
Sol. [Key Concept: $\alpha$ equals the speed of light (numerically $3 \times 10^{8}$ m per unit); the distance is $c \times \ t = 3 \times 10^{8} \times 400$ s $= 400\alpha$ (light takes $6$ min $40$ s $= 400$ s).]
$$\alpha = 3 \times 10^{8}\text{ }m $$Distance $= (400) \times 3 \times 10^{8}\text{ }m = 400\alpha$
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