What is the Venus-Earth distance in α units if light takes 6 min 40s?

400α. Since α=speed of light and time=400s, distance=1α×400s=400α.

Light takes 6 min 40s to travel from Venus to Earth, new unit α equals speed of light — distance in α units

Q: What does 1α unit represent?

1α = 1 light-second = distance light travels in 1 second = 3×10⁸ m.

JEERANKERS

PhysicsUnits

QA new unit $\alpha$ 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 $\alpha$ units if light takes 6 min 40 s to cover this distance?

A) 200α B) 400α C) 300α D) 500αUnits & Measurement

MCQ

✅ Correct Answer

B) 400 α

✓

Solution

Understand the unit α

The unit $\alpha$ is defined as the speed of light. So $1\,\alpha = c = 3\times10^8$ m/s in SI units.

In this new unit system: speed of light $= 1\,\alpha$ per unit time.

Convert time to seconds

$6\text{ min }40\text{ s}=6\times60+40=360+40=400\text{ s}$

Compute distance

$d=c\times t=1\,\alpha\times400\text{ s}=\boxed{400\,\alpha}$

The unit $\alpha$ is essentially a "light-second" — the distance light travels in one second.

📘 Definition of α Unit

The unit $\alpha$ is the speed of light, making this a dimensional analysis problem. Distance $=$ speed $\times$ time $=1\alpha\times t$. So distance in $\alpha$ units numerically equals the travel time in seconds.

💡

Important Concepts

Light-Second Analogy1 light-second = distance light travels in 1 second ≈ 3×10⁸ m. The unit α is essentially 1 light-second. So 400s of travel = 400 α.

Unit Conversion6 min 40 s = 400 s. This is the only conversion needed since α is defined as the speed of light, making d=t numerically in these units.

Other Cosmic Distance Units1 light-year = distance light travels in 1 year. 1 AU ≈ 8.3 light-minutes ≈ 500 light-seconds. Venus-Earth distance varies; 400 light-seconds ≈ 1.2×10¹¹ m.

Dimensional Homogeneity[d] = [α][t] = (m/s)(s) = m. The unit α has dimensions of velocity, so α×s = length unit. Everything is consistent.

FAQs

What is the unit α?

⌄

α is defined as the speed of light c. So 1α = c = 3×10⁸ m/s. Distance = c×t = α×400s = 400α.

Why not use 6 min 40s directly?

⌄

We need seconds for this unit system. 6 min 40s = 6×60+40 = 360+40 = 400s.

Is this similar to a light-year?

⌄

Yes, but smaller. 1 light-year = c × 1 year. Here we have c × 400s = 400 light-seconds.

What is the SI distance?

⌄

d = 3×10⁸ × 400 = 1.2×10¹¹ m = 120 million km.

Is this from JEE Main 2026?

⌄

Yes, this appeared in JEE Main 2026.

🔗