Question

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?​

Answer 1

Explanation:

Given that,

1 Calorie=4.2 J = 4.2 Kg m2 s-2 ...... (i)

As new unit of mass = α Kg

∴ 1 Kg = 1/α new unit of mass

Similarly, 1 m = β-1 new unit of length

1 s = γ-1 new unit of time

Putting these values in (i), we get

1 calorie = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2

= 4.2 α-1 β-2 γ2 new unit of energy (Proved)

Answer 2

$\huge\underline\mathcal\pink{ANSWER}$

Distance between the Sun and the Earth = Speed of light x Time taken by light to cover the distance

Given that in the new unit, speed of light = 1 unit

Given that in the new unit, speed of light = 1 unitTime taken, t = 8 min 20 s = 500 s

∴ Distance between the Sun and the Earth = 1 x 500 = 500 units