Problem 2 on Units & Dimensions

Description:

Problem

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between Sun and the Earth in terms of the new unit if light takes 8 min 20 s to cover the distance?

Solution

Given in the problem,

Speed of light = 1 m/s

With the choice of this speed as new standards, clearly the meaning of old unit ‘meter’ is lost. It considers very large unit of length as ‘meter’ now.

Time taken by the light = 8 min 20 s = 500 s

Distance between sun and earth,

Distance = Speed × Time

Therefore,

Distance = 1(m/s) × 500 (s)

Distance = 500 m

Note − This new fundamental unit of ‘meter’ in the problem, is significantly large compared to the standard meter we are aware of.