The rest distance between Lucknow and Bhopal is 1000 km . A nonstop train travels at 360 km h ⁻¹ . Determine the distance between Lucknow and Bhopal in the train frame.

Step-by-step solution

The rest distance is L₀ = 1000 km = 10^6 m . The speed of the train is v = 360 km h ⁻¹ = 360 5 18 m s ⁻¹ = 100 m s ⁻¹ . According to the length contraction formula, the distance in the train's frame is L = L₀ 1 - v^2 c^2 . Since v c , using the binomial expansion gives L L₀ (1 - v^2 2c^2 ) . The decrease in length is L = L₀ - L = L₀ v^2 2c^2 . Substituting the values: L = 10^6 (100)^2 2 (3 10^8)^2 L = 10¹⁰ 18 10¹⁶ L = 1 18 10⁻⁶ m L 0.0555 10⁻⁶ m = 55.5 nm 56 nm Thus, the distance in the train's frame is 56 nm less