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

Step 1: Understanding the Concept:
Distance is the product of speed and time. In this problem, we are asked to find the distance using a "new unit" system where the speed of light ($c$) is exactly 1.

Step 2: Key Formula or Approach:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Step 3: Detailed Explanation:
1. Convert time to seconds: - 6 minutes = $6 \times 60 = 360$ s - Total time ($t$) = $360 + 40 = 400$ s 2. Apply the formula in the new units: - Speed ($c$) = 1 (unity) - Distance = $1 \times 400 = 400$ units

Step 4: Final Answer:
The distance in the new unit is 400.