A person standing on a platform finds that a train moving with velocity 0.6c takes one second to pass by him. Find

(a) the length of the train as seen by the person and

(b) the rest length of the train.

A suitcase kept on a shop’s rack is measured 50 cm × 25 cm × 10 cm by the shop’s owner. A traveler takes this suitcase in a train moving with velocity 0.6c. If the suitcase is placed with its length along the train’s velocity, find the dimensions measured by

(a) the traveler and

(b) a ground observer

The length of a rod is exactly 1m when measured at rest. What will be its length when it moves at a speed of

(a) 3 × 10⁵ m s^–1

(b) 3 × 10⁶ m s^–1 and

(c) 3 × 10⁷ m s^–1?

An Airplane travels over a rectangular field 100 m × 50m, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?

The rest distance between Patna and Delhi is 1000 km. A nonstop train travels at 360 km h^–1.

(a) What is the distance between Patna and Delhi in the train frame?

(b) How much time elapses in the train frame between Patna and Delhi?