Measured at rest, a rod has an exact length of 1 m . Determine its length when it travels at a speed of 3 10^7 m s ⁻¹ .

Step-by-step solution

Given rest length of the rod, L₀ = 1 m Speed of the rod, v = 3 10^7 m s ⁻¹ Speed of light, c = 3 10^8 m s ⁻¹ Using the length contraction formula: L = L₀ 1 - v^2 c^2 Substituting the given values: L = 1 1 - ( 3 10^7 3 10^8 )^2 L = 1 - (0.1)^2 L = 1 - 0.01 L = (1 - 0.01)^ 1/2 Using the binomial approximation (1 - x)^n 1 - nx for x 1 : L 1 - 1 2 (0.01) L 1 - 0.005 = 0.995 m