The length of a rod is exactly 1 m when measured at rest . What will be its length when it moves at a speed of (a) `3 xx 10^(5)m s ^(-1)` (b) `3 xx 10^(6) m s^(-1)` and ( c) `3 xx 10^(7) m s ^(-1)` ?

Explanation

Given ` L = 1 m , L' = (sqrt 1 - v^(2) / c^(2) `
(a) Here `v = 3 xx 10^(5) m /s `
` L' = 1 xx (sqrt (1 -) (9 xx 10^(10) ) / (9 xx 10^(16)))`
` = (sqrt 1 - 10^(6) ) = 0999995 m`
(b) Here ` v = 3 xx 10^(6) m /s `
` L' = 1 xx (sqrt (1-) (9 xx 10^(12) / 9 xx 10^(16)) `
` = 1 (sqrt 1 -10^(-4) ) `
(c) Here ` v = 3 xx 10^(7) m /s `
L'= 1 xx (sqrt (1-) (9 xx 10^(14) / 9 xx 10^(16)) `
` = 1 (sqrt 1 - 10^(-2))`
` = 0.0049 = 0.995m ` .