A 160m long train is traveling towards a 100m long tunnel A

A 160-m long train is traveling towards a 100-m long tunnel. A trainspotter (me) is standing beside the track and watching.

100 m is the proper length of the tunnel. In which frame of reference is the proper length of the tunnel measured?

Question 2 options:

The train\'s frame of reference.

My frame of reference.

Both my frame of reference and the train\'s frame of reference.

The proper length cannot be measured in this problem.

Please explain reasoning.

Solution

The length of tunnel is contracted relative to observer on the tran\'s reference frame. Becausethe tunnel is in motion relative to the observer.

The tunnel is at rest according to observer on the track frame of reference. Hence the proper length of tunnel is measured by the My frame of reference.