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?
The distance between the Sun and the Earth is 500 units in terms of the new unit of length.
Explanation
This question tests the understanding of units and the relationship between speed, distance, and time. When a new unit of length is defined such that the speed of light becomes unity (1), it means light travels 1 unit of distance in 1 unit of time (second). The distance can be directly calculated as the product of speed and time taken.
Solution Steps
Step 1: Convert the given time into seconds. Time = 8 min 20 s = () + 20 = 480 + 20 = 500 s
Step 2: Apply the relation between distance, speed, and time. Distance = Speed × Time
Step 3: Substitute the values in the new unit system. Since speed of light = 1 unit/s (unity), Distance = = 500 units