### Question 2.5

NCERT Class XI Physics

A new unit of length is chosen such that the speed of light in vacuum is unity. What is 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 ?

### Solution in Detail

$\displaystyle \text{Given: speed of light } = 1 \text{ unit } / \text{s}$

time to cover is $\displaystyle 8 \text{ min } 20 \text{ s } \equiv 500 \text{ s }$

$ \begin{aligned} \implies \text{distance } &= \text{ speed } \times \text{ time}\\ \\ & = 1 \text{ unit } / \text{s} \times 500 \text{ sec}\\ \\ & = 500 \text{ units}\:\underline{Ans} \end{aligned} $

### Physical Concept and Assumptions

(for Advanced Students)

- Physical Concept
- The speed of light in vacuum has been given as 1, and the time taken to cover the distance between earth and sun as 500 seconds. So by speed formula, the distance in new units would be speed x time = 1 (new units/s) × 500 s = 500 (units) - answer!
- Assump 1: Speed of light assumed unity per second
- Explanation: The speed of light has been given as unity but it is not clear whether it is in terms of seconds? or minutes? or hours? We have assumed it to be in seconds.
- Asump 2: Sun and Earth are point objects with negligible atmosphere
- Explanation: We will have to neglect the atmospheres of Earth and Sun and treat both of them as point objects with negligible radii in comparison to the distance between them. So we can assume that they are separated ONLY by vacuum. Hence, the distance between them would be the distance covered by light in vacuum in 8 min and 20 seconds = 500 seconds.

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