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.
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.
Updated On: Apr 13, 2026
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Correct Answer: 400
Solution and Explanation
Concept:
The speed of light in vacuum is
\[
c = 3 \times 10^8 \ \text{m/s}
\]
The new unit of length \(\alpha\) is defined as the distance travelled by light in 1 second.
\[
1\alpha = c \times 1\,\text{s}
\]
Thus,
\[
1\alpha = 3\times10^8 \ \text{m}
\]
Step 1:Calculate the total time taken by light. \[ t = 6 \text{ min } 40 \text{ s} \] \[ t = 6\times60 + 40 = 360 + 40 = 400 \text{ s} \]
Step 2:Find the actual distance between Venus and Earth. \[ d = vt \] \[ d = (3\times10^8)(400) \] \[ d = 12\times10^{10} \ \text{m} \]
Step 3:Convert the distance into the new unit. Since \[ 1\alpha = 3\times10^8 \text{ m} \] \[ n\alpha = 12\times10^{10} \] \[ n(3\times10^8) = 12\times10^{10} \] \[ n = 400 \] \[ \boxed{400\alpha} \]
Step 1:Calculate the total time taken by light. \[ t = 6 \text{ min } 40 \text{ s} \] \[ t = 6\times60 + 40 = 360 + 40 = 400 \text{ s} \]
Step 2:Find the actual distance between Venus and Earth. \[ d = vt \] \[ d = (3\times10^8)(400) \] \[ d = 12\times10^{10} \ \text{m} \]
Step 3:Convert the distance into the new unit. Since \[ 1\alpha = 3\times10^8 \text{ m} \] \[ n\alpha = 12\times10^{10} \] \[ n(3\times10^8) = 12\times10^{10} \] \[ n = 400 \] \[ \boxed{400\alpha} \]
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