A new unit of length is chosen such that the speed of light in vacuum

1.	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» New unit of length = 3 × 108 ms^-1 Distance between the Earth and the sun = (8 min 20 s) x 3 x 10⁸ ms^-1 = 500 × 3 × 10⁸ ms^-1 ∴ Distance between the Earth and the Sun in terms of the new units = ((500 x 3 x 10⁸)/(3 x 10⁸)) = 500 new units.

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»

New unit of length = 3 × 108 ms^-1

Distance between the Earth and the sun

= (8 min 20 s) x 3 x 10⁸ ms^-1

= 500 × 3 × 10⁸ ms^-1

∴ Distance between the Earth and the Sun in terms of the new units

= ((500 x 3 x 10⁸)/(3 x 10⁸))

= 500 new units.