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 ?

Question

Mass = \( (28 \pm 0.01) \, \text{g} \), Volume = \( (5 \pm 0.1) \, \text{cm}^3 \). What is the percentage error in density?

Answer 1

Given:

In the new system of units, the speed of light in vacuum is chosen as:
c = 1 unit of length per second

Time taken by light to travel from the Sun to the Earth:

8 minutes 20 seconds

Convert into seconds:

8 minutes = 8 × 60 = 480 s
So, total time = 480 + 20 = 500 s

Step 1: Use the relation distance = speed × time

Distance = c × time

Since c = 1 in the new unit system:

Distance = 1 × 500

Distance = 500 units of length

Final Answer:

The distance between the Sun and the Earth in the new unit of length is
500 units.

Solution and Explanation