Question

A suitcase kept on a shop's rack is measured 50 cm $\times$ 25 cm $\times$ 10 cm by the shop's owner. A traveller 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 traveller and (b) a ground observer.

Answer 1

Given : $v=0.6c$ $l_o=50$ cm $b_o=25$ cm $h_o=10$ cm

(a) Suitcase is at rest as seen by the traveller ( or train frame), thus he measures the rest dimensions of the suitcase i.e 50 cm x 25 cm x 10 cm

(b) Relativity states that length of the moving object parallel to its motion gets shortened by a factor $\sqrt{1-(v/c{)}^2}$ but the length perpendicular to the motion remains the same.

Thus length of the suitcase seen by ground observer $l=l_o\sqrt{1-(v/c{)}^2}=50\times \sqrt{1-(0.6{)}^2}=40$ cm

Thus he measures the moving dimensions of the suitcase i.e 40 cm x 25 cm x 10 cm