Question

How fast must a meter stick be moving if its length is observed to shrink to 0.7 m?

Answer 1

2.14×10⁸ m/s

Step-by-step explanation:

L=Required Length=0.7 m

L₀=Initial length=1 m

c=speed of light=3×10⁸ m/s

`From\ Lorentz\ Contraction\ relation\\L=L_0\sqrt{1-\frac {v^2}{c^2}}\\\Rightarrow 0.7=1\sqrt {1-\frac {v^2}{c^2}}\\\Rightarrow 0.49=1-\frac {v^2}{c^2}\\\Rightarrow 0.49-1=-\frac {v^2}{c^2}\\\Rightarrow -0.51=-\frac {v^2}{c^2}\\\Rightarrow 0.51=\frac {v^2}{c^2}\\\Rightarrow v^2=0.51* c^2\\\Rightarrow v=√(0.51) * c\\\Rightarrow v=0.71* 3* 10^8\\\Rightarrow v=2.14* 10^8\ m/s\\\therefore velocity\ of\ stick\ should\ be\ 2.14* 10^8\ m/s`