Question

A new unit of length is so choses that the speed of light in vacuum is unity. Calculate the distance (in the new unit) between sun and the earth if light takes 8 min and 20 seconds to reach earth from sun.

Answer 1

Answer:

as given in the question

1m=speed of light=3×10^8

velocity(v)=distance(d)÷time(t)

d=vt = 3×10^8m\s ×8(60)+20

d=1500×10^8 m

now,

n1 u1=n2 u2

1500×10^8 m=n2(3×10^8 m)

1500×10^8÷3×10^8=n2

n2=500

Answer 2

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 20s to cover this distance.

Answer:-

Speed of light = 1 new unit ,

Time taken = 8 min + 20s

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎= 480s + 20s

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎= 500s

Now,

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎D = S/T

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎ ‎S*T = D

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎1 new unit/sec * 500s = D

‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎‎‎‎ ‎ ‎ ‎ ‎ ‎D = 500 new unit

Therefore, The distance between sun and earth is 500 new unit.