Answer:
L₀ = 0.0022 m = 2.2 mm
Explanation:
Here, we will use the length contraction formula from the theory of relativity presented by Einstein:
[tex]L = L_o\sqrt{1-\frac{v^2}{c^2}}[/tex]
where,
L = Relative length = 1.57 mm = 0.00157 m
L₀ = actual length at rest = ?
c = speed of light
v = relative speed = 70% of c = 0.7 c
Therefore,
[tex]0.00157\ m = L_o\sqrt{1-\frac{(0.7\ c)^2}{c^2} }\\\\L_o = \frac{0.00157\ m}{\sqrt{1-0.49}}[/tex]
L₀ = 0.0022 m = 2.2 mm