Question

A suitcase kept on a shop's rack is measured 50 cm × 25 cm × 10 cm by the shop's owner. A traveller takes this suitcase in 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

Explanation:

It is given:

Suitcase has the length, l = 50 cm

Suitcase has the breadth, b = 25 cm

Suitcase has the height, h = 10 cm

Train’s velocity, v = 0.6c

(a) In the train, the observer notices the similar values of b, l and h. This is due to the fact that the suitcase will be in rest with reference to the traveller.

(b) With reference to the ground observer, the suitcase moves with 0.6 c speed. The length’s component is parallel to the velocity that experiences reduction, but the perpendicular components like the height and the breadth will always stay the same.

Hence, the train’s length that is parallel to the velocity keeps changing, while the height and the breadth stay the same.

$\mathrm{L}^{\prime}=11-\mathrm{v} 2 \mathrm{c} 2=501-0.36=50 \times 0.8=40 \mathrm{cm}$

So, the ground observer measures the proportions and they are $25 \mathrm{cm} \times 40 \mathrm{cm} \times 10 \mathrm{cm}$