Answer:
[tex]L_0\approx1.0328\ m[/tex]
Explanation:
Given:
Since the object is moving with a velocity comparable to the velocity of light with respect to the observer therefore the length will appear shorter according to the theory of relativity.
Mathematical expression of the theory of relativity for length contraction:
[tex]L=\frac{L_0}{\gamma}[/tex]
where:
L = relativistic length
[tex]L_0=[/tex] original length at rest
[tex]\gamma =[/tex] Lorentz factor [tex]=\frac{1}{\sqrt{1-\frac{v^2}{c^2} } }[/tex]
[tex]\Rightarrow 1=\frac{L_0}{\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }}[/tex]
[tex]L_0=\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }[/tex]
[tex]L_0\approx1.0328\ m[/tex]