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
(a) The traveler is traveling in the same frame in which suitcase is travelling. So, the dimensions of the suitcase for the traveler will remain same.
(b) The observer who is on the ground will not see the same dimensions of the suitcase. It is because the frame of reference of observer and the suitcase is different. The suitcase is in the frame of reference which is moving with the speed of 0.6c. Since, the suitcase is placed with its length along the train’s velocity, the changes will be observed in the length only.
Length of the suitcase= 50cm
Breadth = 25cm
Height = 10cm
Velocity= 0.6c
Therefore, the length observed by the observer on the ground will be less than the original length of the suitcase. The dimensions will be 40cm x 25cm x 10cm.