Class 11 NCERT PHYSICS • Chapter 1: Units and Measurement • Question 5

QUESTION 5

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?

SOLUTION

We need to calculate the astronomical distance in new units where the speed of light is defined as unity.

Concept: Distance-speed-time relationship

The distance traveled by an object at a constant speed is determined by the distance-speed-time relationship:

d = v \cdot t

where $d$ is the distance, $v$ is the speed, and $t$ is the time duration. In this new system of units, the speed of light $c$ is defined as unity ( $1$ ).

Given:

Speed of light in the new unit system, $c = 1\,\text{unit} \cdot \text{s}^{-1}$
Time taken by light to travel from the Sun to Earth, $t = 8\,\text{min}\ 20\,\text{s}$

Solving:

First, we convert the total time duration into seconds to maintain consistency with the unit of speed:

\begin{aligned} t &= 8\,\text{min} + 20\,\text{s} \\ &= (8 \times 60)\,\text{s} + 20\,\text{s} \\ &= 480\,\text{s} + 20\,\text{s} \\ &= 500\,\text{s} \end{aligned}

Next, we calculate the distance $d$ using the defined speed of light:

\begin{aligned} d &= c \cdot t \\ &= 1\,\text{unit} \cdot \text{s}^{-1} \times 500\,\text{s} \\ &= 500\,\text{units} \end{aligned}

Answer

500\,\text{units}