Question

It takes time $8$min for light to reach from the sun to the sun to the earth surface. If the speed of light is taken to be $3 \times {10^8}m{s^{ - 1}}$, find the order of magnitude of distance from the sun to the earth in km.
$A{.10^7}km \\\ B.15 \times {10^8}km \\\ C{.10^5}km \\\ D{.10^9}km \\\$

Answer 1

Hint: Here we will proceed by using the formula of velocity. Then by applying the conditions given in the question we will get our answer.

Formula used: $v = \dfrac{s}{t}$
Where, v is velocity
s is displacement
t is time taken.

Complete step-by-step solution -

Here, it is given that,
Time t
$= 8\min$
Converting in seconds, $8 \times 60 = 480s$
Velocity, $v = 3 \times {10^8}$
We know that,
The speed is defined as:
$v = \dfrac{d}{t}$
The distance is the product of the speed of time, its unit is meter.
We can also write it as, the distance is
$d = v \times t$
$d = 3 \times {10^8} \times 480$
$= 1440 \times {10^8}$
$d = 1.44 \times {10^{11}}m$
By converting it into km, we get
$d = 1.44 \times \dfrac{{{{10}^{11}}}}{{{{10}^3}}}km \\\ d = 1.44 \times {10^8}km \\\$
Hence, the distance from the sun to the earth is $1.44 \times {10^8}km$

Note – Whenever we come up with this type of question, one must know that the time will not be exactly correct and the distance between earth and sun is going to change as earth revolves in elliptical orbit. Thus all the scientific calculations are not exact but approximate.