Question

The length of a rod is exactly 1 m when measured at rest. What will be its length it moves at a speed of (a) $3\times {10}^{5}m{s}^{-1}$ (b) $3\times {10}^{6}m{s}^{-1}$ (c) $3\times {10}^{7}m{s}^{-1}$

Answer 1

Given : Rest length $L_o=1$ m

Length of the moving rod $L=L_o\sqrt{1-(\frac{v}{c}{)}^2}$ where $c=3\times {10}^8$ m/s

(a) : $v=3\times {10}^5$ m/s $⟹L_a=$ $1\times \sqrt{1-(\frac{3\times {10}^5}{3\times {10}^8}{)}^2}=0.99999$ m

(b) : $v=3\times {10}^6$ m/s $⟹L_b=$ $1\times \sqrt{1-(\frac{3\times {10}^6}{3\times {10}^8}{)}^2}=0.99995$ m

(c) : $v=3\times {10}^7$ m/s $⟹L_b=$ $1\times \sqrt{1-(\frac{3\times {10}^7}{3\times {10}^8}{)}^2}=0.99499$ m