Question

A new unit of length is chosen such that the speed of light in a vacuum will be unity. Calculate the distance between the sun and the earth in terms of the new unit when the light is taking $8\min$ and $20\sec$ to cover this distance?
$\begin{aligned} & A.100unit \\\ & B.500unit \\\ & C.2unit \\\ & D.20unit \\\ \end{aligned}$

Answer 1

First of all convert the time taken into second. Distance between the Sun and the Earth can be found by taking the product of the speed of light and the time taken by light to cover the distance. Substitute the values in it. This all will help you in solving this question.

Complete step by step answer:
It has been mentioned in the question that the time taken by the light to cover the distance is,
$t=8\min 20s$
Let us convert the time into the unit of second. That can be shown as,
$t=8\times 60+20=480+20=500s$
Now we have to find the distance between the sun and the earth. The velocity of light has been given in the question as unity. Therefore we can write that,
$C=1unit$
Distance between the Sun and the Earth will be equivalent to the speed of light multiplied with the time taken by the light to cover the distance. That is we can express this in form of equation as,
$d=C\times t$
Substitute the values in it will be written as,
$d=1\times 500s=500unit$
Therefore the distance between the earth and the sun has been obtained as $500units$. This has been given in the options as option B.

Note: The velocity is the time rate of variation of the displacement. Distance covered is the total length of the path traversed by a body. The displacement is the shortest distance between the initial and final points. Time rate of variation of distance is known as speed.