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 8min and 20s to cover this distance​

Answer 1

Answer:

formula

distance = speed * time

speed = 1 unit/sec

time = 8*60+20 = 500sec

distance = 1*500 = 500unit

hope it helps

Answer 2

Answer:

500 units of new length

Explanation:

The speed of light in vacuum in S.I. unit is 3×10⁸ ms⁻¹.

The new unit of length is 3×10⁸ m in which the speed of light is unity.

Now, in S.I. unit , the distance between sun and earth is :

speed of light × time taken = 3×10⁸ ms⁻¹ × 8 min 20 s

                                             = 3×10⁸ ms⁻¹ × 500s

                                             = 1.5 × 10¹¹ m

We know that if n₁ and n₂ be the numerical values of quantity in units u₁ and u₂ respectively , then

n₁ (u₁) = n₂ (u₂)

Here,

n₁ = 1.5 × 10¹¹ , u₁ = m , u₂ = 3×10⁸ m , n₂=?

∴1.5 × 10¹¹ (m) = n₂ (3 × 10⁸m)

 n₂ = $\frac{(1.5*10^{11}m)}{(3.0*10^{8}m)}$

      = 500

Therefore the distance between the sun and the earth is 500 new units of length.