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

Step-by-step solution

The rest distance between Lucknow and Bhopal 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 . The time elapsed in the ground frame is: t = L₀ v = 10^6 100 = 10^4 s Converting this time into minutes: t = 10000 60 min = 500 3 min The time elapsed in the train frame is the proper time t₀ , given by the time dilation formula: t₀ = t 1 - v^2 c^2 The difference in time between the two frames is: t - t₀ = t (1 - 1 - v^2 c^2 ) Since v c , using the binomial expansion (1