Physics Q26 – JEE-MAIN 2026

Home Physics Units & MeasurementsQuestion #559

A new unit (

α

) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of

α

units if light takes 6 min, 40 s to cover this distance ?

Clue 1 of 3: Understand the new unit

The problem defines a new unit of length, $α$ , in relation to the speed of light.

🧠 Full Solution Path

Step 1: Convert time to seconds✦ Active

The time taken for light to cover the distance is given as 6 minutes and 40 seconds. Convert this total time into seconds.

t = 6 min + 40 s = (6 \times 60) s + 40 s = 360 s + 40 s = 400 s

Step 2: Interpret the new unit of length (

α

)○ Expand

The problem states that a new unit ( $α$ ) of length is chosen such that it is equal to the speed of light in vacuum. This implies that $1 α$ is the distance light travels in 1 second. Therefore, the speed of light $c$ can be expressed as:

c = 1 \frac{α}{second}

💡 Teacher's Secret Hint

This definition means that in this new system of units, the numerical value of the speed of light is 1 when time is in seconds and distance is in $α$ units.

Step 3: Calculate the distance○ Expand

Now, use the formula $D = c \times t$ to find the distance between Venus and Earth in terms of $α$ units.

D = c \times t = (1 \frac{α}{second}) \times (400 seconds) = 400 α

Thus, the distance between Venus and Earth is $400 α$ units.

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Physics Question 26 – JEE-MAIN 2026

Clue 1 of 3: Understand the new unit

🧠 Full Solution Path