First slide

Physical quantities and units

Question

A new unit of length is chosen such that the speed of light in vacuum is unity. Then the distance between the sun and the earth in terms of the new unit, if light takes 8 min and 20 s to cover this distance?

Moderate

A

300 new unit of length
B

500 new unit of length
C

600 new unit of length
D

None of these

Solution

The speed of light in vacuum (c) =1 $= (n e w u n i t o f l e n g t h s^{- 1})$
Time taken by light to reach the earth
t =8 min + 20 s
= (8 $\times$ 60 + 20) s = 500s
$∴$ Distance between the sun and the earth
= Speed of light $\times$ Time
x = c $\times$ t
$= 1 (n e w u n i t o f l e n g t h s^{- 1}) \times 500 s$
=500 new unit of length

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