Chapter 6, Problem 94A

Interpretation Introduction

Interpretation:

The number of round trips done by light between Earth and the sun in one day is to be calculated.

Concept Introduction :

The relation between velocity, time and distance is as follows:

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

Answer to Problem 94A

Light can complete 86 round trips between the Earth and the Sun in 24 hr.

Explanation of Solution

Distance between Earth and Sun: $1.5\times {10}^8\text{ km}$

Speed of light: $3.0\times {10}^8\text{m}/\text{s}$

Calculate distance in m as,

  $\begin{array}{c}\text{distnace}=1.5\times {10}^8\bcancel{\text{km}}\times \frac{{10}^3\text{ m}}{1\bcancel{\text{km}}}\\ =1.5\times {10}^{11}\text{ m}\end{array}$

In a round trip, distance will be double. So, distance will be $3.0\times {10}^{11}\text{ m}$ .

In one day 24 hrs are there.

Calculate no. of seconds in one day as,

  $\begin{array}{c}24\text{ hr}=24\text{ hr}\times \frac{60\text{ min}}{1\text{ hr}}\times \frac{60\text{ s}}{1\text{ min}}\\ =\text{86,400 s}\end{array}$

Calculate time taken by light to calculate one round trip

  $\begin{array}{c}\text{speed}=\frac{\text{distance}}{\text{time}}\\ \text{time}=\frac{\text{distance}}{\text{speed}}\\ =\frac{3.0\times {10}^{11}\text{ m}}{3.0\times {10}^8\text{m}/\text{s}}\\ =1000\text{ s}\end{array}$

So, in trip 1000 s is required.

So, no. of the round trip can be done by light is,

  $\begin{array}{c}\text{no}\text{. of round trip}=\frac{\text{86,400 s}}{1000\text{s}/\text{trip}}\\ =86.4\text{ trip}\\ =86\text{ trip}\end{array}$

So, light can complete 86 round trips between the Earth and the Sun in 24 hr.