Question

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is: ____.

• A. 500
• B. 3 $\times$ 10⁸
• C. 400
• D. 3 $\times$ 10¹⁰

Hint:

This "new unit" is essentially a "light-second." One light-second is the distance light travels in one second. Since it takes 400 seconds, the distance is 400 light-seconds.

Answer 1

The Correct Option is C

To solve the problem of finding the distance between the Sun and the Earth in the new unit where the speed of light is taken as unity, follow these steps:

1. Understanding the Problem: The question states that the speed of light in a vacuum is taken as unity (1 unit per time unit). Therefore, in this scenario, the distance travelled by light in a given time is equal to the time itself.
2. Given Time Duration: Light takes 6 minutes and 40 seconds to reach Earth from the Sun. Convert this time duration fully into seconds:
   • 6 minutes = 6 × 60 = 360 seconds
   • Additional 40 seconds
   • Total Time = 360 + 40 = 400 seconds
3. Distance Calculation: Since the speed of light is taken as unity, the distance travelled by light in 400 seconds is 400 units.
4. Conclusion: Therefore, the distance between the Sun and the Earth in the new unit is 400.