Question

A new unit (\(\alpha\)) of length is chosen such that it is equal to the distance travelled by light in vacuum in 1 second. What is the distance between Venus and Earth in terms of this new unit. If light takes 6 min 40 sec to cover the distance.

Answer 1

Correct Answer: 400

Step 1: Understanding the Concept:
The question defines a unit based on the speed of light.
Distance is the product of speed and time.
We need to express the given time in seconds to compare it with the unit definition.
Step 2: Key Formula or Approach:
Distance $d = v \times t$, where $v = c$ (speed of light).
New unit $1\ \alpha = c \times 1 \text{ s}$.
Step 3: Detailed Explanation:
Time taken by light to reach Earth from Venus is given as $t = 6 \text{ min } 40 \text{ sec}$.
Converting this time strictly into seconds:
\[ t = (6 \times 60) + 40 = 360 + 40 = 400 \text{ s} \]
The total distance covered is $d = c \times 400 \text{ s}$.
Since $c \times 1 \text{ s} = 1 \text{ unit}$, we can write:
\[ d = 400 \times (c \times 1 \text{ s}) = 400 \text{ units} \]
Step 4: Final Answer:
The distance is 400 units.