Question

It takes 8 minutes and 20 seconds for sunlight to reach the earth, find the distance between the earth and the sun. The velocity of light is $3\times {{10}^{8}}{m}/{s}\;$.

(a). $15\times {{10}^{10}}m$

(b). $25\times {{10}^{10}}m$

(c). $30\times {{10}^{10}}m$

(d). $5\times {{10}^{10}}m$

Answer 1

Hint: We know that the relation between speed, distance and time can be given by using the formula,

$\text{speed}=\dfrac{\text{distance}}{\text{time}}$. But before using this formula we have to convert time which is 8 minutes into seconds because all our units should be in the MKS unit system.

Formula used: $\text{speed}=\dfrac{\text{distance}}{\text{time}}$

Complete step by step answer:

 In the question we are given that sun rays take 8 minutes and 20 seconds to reach the Earth from the Sun and we have to find the distance between Earth and Sun. So, we will use the formula which is given as,

$\text{speed}=\dfrac{\text{distance}}{\text{time}}$

Or $\text{s}=\dfrac{\text{d}}{\text{t}}$

Where, s is speed in ${m}/{s}\;$, d is distance in metre, and t is time in seconds.

Now, we are given that time taken by rays is 8 minutes so, we will convert minutes into seconds which is given as,

$1\ \text{minute}=60\ \text{seconds}$

So, $8\ \text{minute and 20 seconds}=8\times 60\ \text{seconds+20}=480+20\ \sec $

$8\ \text{minute and 20 seconds}=500\sec $

Now, t is 500 sec, and s is $3\times {{10}^{8}}{m}/{s}\;$, substituting these values in main expression we will get,

$3\times 1{{0}^{8}}=\dfrac{\text{d}}{500}$

$d=500\times 3\times {{10}^{8}}=15\times {{10}^{10}}m$

Thus, the distance between Earth and Sun is $15\times {{10}^{10}}m$.

Hence, option (a) is correct.

Note: This question can also be solved by using the relation between velocity, time and distance, but in that considering the velocity of light constant is the key point each student should consider otherwise, they might make mistakes in that. The above solution is more preferable and less time consuming also.