Question

Light takes approximately $ 8 $ minutes to reach the earth from the Sun. The distance between earth and Sun is______________. (speed of light $ = 3 \times {10^8}m{s^{ - 1}} $ )
(A) $ 1440 \times {10^8}m $
(B) $ 14 \times {10^8}m $
(C) $ 140 \times {10^8}m $
(D) $ 4 \times {10^8}m $

Answer 1

Hint: To solve this question, we need to use the basic formula of the speed in terms of the distance covered and the time taken. Substituting the values given in the question into the formula, we can get the required distance between earth and Sun.

Formula used: The formula which has been used in solving this question is given by
 $\Rightarrow v = \dfrac{d}{t} $, here $ v $ is the speed, $ d $ is the distance covered in $ t $ time.

Complete step by step answer
We know that the speed of a particle is defined as the distance covered by the particle per unit time.
So we have
 $\Rightarrow v = \dfrac{d}{t} $
So the distance is given by
 $\Rightarrow d = vt $..........................(1)
Now, according to the question, the light is taking approximately $ 8 $ minutes to reach from the earth to the sun. So we have
 $\Rightarrow t = 8\min $
We know that $ 1\min = 60s $. Therefore we have
 $\Rightarrow t = 8 \times 60s $
 $ \Rightarrow t = 240s $ ………………...(2)
Also, the speed of the light is given to be $ 3 \times {10^8}m{s^{ - 1}} $. That is,
 $\Rightarrow v = 3 \times {10^8}m{s^{ - 1}} $ ………………….(3)
Substituting (2) and (3) in (1) we get
 $\Rightarrow d = 3 \times {10^8} \times 240 $
 $ \Rightarrow d = 1440 \times {10^8}m $
This is the distance covered by the light in the given time. Since in the given time the light reaches from the earth to the sun, this distance will be equal to the distance between the earth and the sun.
Thus the distance between earth and sun is equal to $ 1440 \times {10^8}m $.

Hence, the correct answer is option A.

Note
We should not forget to convert all the values of the quantities into their respective SI units. For example, the time in this question was given in minutes, which is not an SI unit. So it was supposed to be converted to seconds.